Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22581501 | C2 | semidirect |
| 2. C4×#14555786 | C2 | semidirect |
| 3. #22581275 | C2 | semidirect |
| 4. #22581238 | C2 | semidirect |
| 5. #22581234 | C2 | semidirect |
| 6. #22581145 | C2 | semidirect |
| 7. #22581097 | C2 | semidirect |
| 8. #22581062 | C2 | semidirect |
| 9. #22581054 | C2 | semidirect |
| 10. #22581009 | C2 | semidirect |
| 11. #460×C139 | C2 | semidirect |
| 88. D556 | #41 | semidirect |
| 106. Q8×C139 | #41 | semidirect |
| 144. C139 | #3115 | semidirect |
| 151. #460 | D139 | semidirect |
| 233. Q8 | #14555784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581501 | 2 |
| C4×#14555786 | 2 |
| #22581275 | 2 |
| #22581238 | 2 |
| #22581234 | 2 |
| #22581145 | 2 |
| #22581097 | 2 |
| #22581062 | 2 |
| #22581054 | 2 |
| #22581009 | 2 |
| #460×C139 | 2 |
| #3115 | 139 |