Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
382 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581682 | C2 | semidirect |
| 3. #22581316 | C2 | semidirect |
| 4. #22581299 | C2 | semidirect |
| 5. #22581251 | C2 | semidirect |
| 6. #22581234 | C2 | semidirect |
| 7. #22581151 | C2 | semidirect |
| 8. #22581080 | C2 | semidirect |
| 9. #22581054 | C2 | semidirect |
| 10. C4×#14555772 | C2 | semidirect |
| 11. #460×C139 | C2 | semidirect |
| 91. Q8×C139 | #41 | semidirect |
| 124. C139 | #3368 | semidirect |
| 133. #460 | D139 | semidirect |
| 204. Q8 | #14555784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581682 | 2 |
| #22581623 | 2 |
| #22581316 | 2 |
| #22581299 | 2 |
| #22581251 | 2 |
| #22581234 | 2 |
| #22581151 | 2 |
| #22581080 | 2 |
| #22581054 | 2 |
| C4×#14555772 | 2 |
| #460×C139 | 2 |
| #3368 | 139 |