Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22581678 | C2 | semidirect |
| 4. #22581258 | C2 | semidirect |
| 7. #22581160 | C2 | semidirect |
| 8. C8×Dic278 | C2 | semidirect |
| 9. #22581045 | C2 | semidirect |
| 11. #487×C139 | C2 | semidirect |
| 115. C139 | #3364 | semidirect |
| 120. #487 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581678 | 2 |
| #22581677 | 2 |
| #22581309 | 2 |
| #22581258 | 2 |
| #22581230 | 2 |
| #22581178 | 2 |
| #22581160 | 2 |
| C8×Dic278 | 2 |
| #22581045 | 2 |
| C4×#14555774 | 2 |
| #487×C139 | 2 |
| #3364 | 139 |