Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
284 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #22580908 | C2 | semidirect |
| 5. #22580725 | C2 | semidirect |
| 6. #22580723 | C2 | semidirect |
| 7. #405×C139 | C2 | semidirect |
| 15. C2×#14555768 | C4 | semidirect |
| 16. C2×C8×D139 | C4 | semidirect |
| 18. #17984760 | C4 | semidirect |
| 19. #17984758 | C4 | semidirect |
| 106. C139 | #1757 | semidirect |
| 112. #405 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984848 | 2 |
| #22580935 | 2 |
| #22580926 | 2 |
| #22580908 | 2 |
| #22580725 | 2 |
| #22580723 | 2 |
| #405×C139 | 2 |
| #1757 | 139 |