Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. C4×#14555785 | C2 | semidirect |
| 2. #22581274 | C2 | semidirect |
| 3. #22581235 | C2 | semidirect |
| 4. #22581230 | C2 | semidirect |
| 5. #22581150 | C2 | semidirect |
| 6. #22581145 | C2 | semidirect |
| 7. #22581096 | C2 | semidirect |
| 8. #22581063 | C2 | semidirect |
| 9. #22581053 | C2 | semidirect |
| 10. #22581010 | C2 | semidirect |
| 11. #532×C139 | C2 | semidirect |
| 85. Dic278 | #41 | semidirect |
| 87. D556 | #41 | semidirect |
| 144. C139 | #3115 | semidirect |
| 146. #532 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14555785 | 2 |
| #22581274 | 2 |
| #22581235 | 2 |
| #22581230 | 2 |
| #22581150 | 2 |
| #22581145 | 2 |
| #22581096 | 2 |
| #22581063 | 2 |
| #22581053 | 2 |
| #22581010 | 2 |
| #532×C139 | 2 |
| #3115 | 139 |