Finite Group DatabasebetaFinite Group DatabasebetaOrder 2368.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#10596962 | C2 | semidirect |
| 2. #11924567 | C2 | semidirect |
| 3. #11924566 | C2 | semidirect |
| 4. #11924562 | C2 | semidirect |
| 5. #11924561 | C2 | semidirect |
| 6. #11924556 | C2 | semidirect |
| 7. C2×#10596934 | C2 | semidirect |
| 8. C2×#41×C37 | C2 | semidirect |
| 12. #41×C37 | C22 | semidirect |
| 13. C2×Q8×C37 | C22 | semidirect |
| 15. C2×D4×C37 | C22 | semidirect |
| 22. #10596962 | C22 | semidirect |
| 23. C2×D148 | C22 | semidirect |
| 25. C2×Dic74 | C22 | semidirect |
| 26. #10596942 | C22 | semidirect |
| 27. #10596941 | C22 | semidirect |
| 28. #10596940 | C22 | semidirect |
| 29. #10596939 | C22 | semidirect |
| 30. #10596934 | C22 | semidirect |
| 31. #10596934 | C22 | semidirect |
| 32. C2×#64436 | C22 | semidirect |
| 82. C37 | #575 | semidirect |
| 84. C2×#41 | D37 | semidirect |
| 98. #41 | C2×D37 | semidirect |
| 100. C2×Q8 | C2×D37 | semidirect |
| 104. C2×D4 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10596962 | 2 |
| #11924567 | 2 |
| #11924566 | 2 |
| #11924562 | 2 |
| #11924561 | 2 |
| #11924556 | 2 |
| C2×#10596934 | 2 |
| C2×#41×C37 | 2 |
| #575 | 37 |