Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1152 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 171 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. #22599327 | C2 | semidirect |
| 2. #22598804 | C2 | semidirect |
| 3. #22587646 | C2 | semidirect |
| 4. #22587629 | C2 | semidirect |
| 5. #22586964 | C2 | semidirect |
| 6. #22586938 | C2 | semidirect |
| 7. C2×H(3,𝔽4)×C71 | C2 | semidirect |
| 10. #17986549 | C22 | semidirect |
| 11. #17986394 | C22 | semidirect |
| 12. #17986389 | C22 | semidirect |
| 13. #17986389 | C22 | semidirect |
| 15. #17986358 | C22 | semidirect |
| 19. #17986056 | C22 | semidirect |
| 20. C4×#11765849 | C22 | semidirect |
| 21. #17985739 | C22 | semidirect |
| 22. #17985739 | C22 | semidirect |
| 42. #14556128 | C23 | semidirect |
| 43. #14556125 | C23 | semidirect |
| 51. #14556039 | C23 | semidirect |
| 52. #14556039 | C23 | semidirect |
| 207. C2×H(3,𝔽4) | D71 | semidirect |
| 214. C71 | #18992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599327 | 2 |
| #22598804 | 2 |
| #22587646 | 2 |
| #22587629 | 2 |
| #22586964 | 2 |
| #22586938 | 2 |
| C2×H(3,𝔽4)×C71 | 2 |
| #18992 | 71 |