Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11924529 | C2 | semidirect |
| 2. #11924529 | C2 | semidirect |
| 3. #11924522 | C2 | semidirect |
| 4. #11924520 | C2 | semidirect |
| 5. #11924519 | C2 | semidirect |
| 6. #11924518 | C2 | semidirect |
| 7. #11924515 | C2 | semidirect |
| 8. #11924513 | C2 | semidirect |
| 10. C4×C22⋊D37 | C2 | semidirect |
| 11. #11924496 | C2 | semidirect |
| 12. #11924495 | C2 | semidirect |
| 13. #11924492 | C2 | semidirect |
| 14. C2×C22⋊Dic37 | C2 | semidirect |
| 15. C2×C22⋊C4×C37 | C2 | semidirect |
| 24. C2×C4×D37 | C22 | semidirect |
| 25. C2×Dic74 | C22 | semidirect |
| 37. #10596938 | C22 | semidirect |
| 38. #10596938 | C22 | semidirect |
| 39. #10596938 | C22 | semidirect |
| 40. C4⋊Dic37 | C22 | semidirect |
| 41. C4⋊Dic37 | C22 | semidirect |
| 42. C4⋊Dic37 | C22 | semidirect |
| 43. #10596936 | C22 | semidirect |
| 44. #10596936 | C22 | semidirect |
| 45. #10596936 | C22 | semidirect |
| 46. #10596936 | C22 | semidirect |
| 47. #10596936 | C22 | semidirect |
| 48. C4×Dic37 | C22 | semidirect |
| 49. C4×Dic37 | C22 | semidirect |
| 50. C4×Dic37 | C22 | semidirect |
| 111. C37 | #551 | semidirect |
| 126. C2×C22⋊C4 | D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11924529 | 2 |
| #11924522 | 2 |
| #11924520 | 2 |
| #11924519 | 2 |
| #11924518 | 2 |
| #11924515 | 2 |
| #11924513 | 2 |
| #11924505 | 2 |
| C4×C22⋊D37 | 2 |
| #11924496 | 2 |
| #11924495 | 2 |
| #11924492 | 2 |
| C2×C22⋊Dic37 | 2 |
| C2×C22⋊C4×C37 | 2 |
| #551 | 37 |