Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. #22581361 | C2 | semidirect |
| 4. #22581360 | C2 | semidirect |
| 5. #22581355 | C2 | semidirect |
| 6. #22581352 | C2 | semidirect |
| 7. #22581352 | C2 | semidirect |
| 11. #499×C139 | C2 | semidirect |
| 43. #14555768 | Q8 | semidirect |
| 44. #14555768 | Q8 | semidirect |
| 99. C139 | #3166 | semidirect |
| 108. #499 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581509 | 2 |
| #125×D139 | 2 |
| #22581361 | 2 |
| #22581360 | 2 |
| #22581355 | 2 |
| #22581352 | 2 |
| #22580994 | 2 |
| #22580992 | 2 |
| C4×#14555768 | 2 |
| #499×C139 | 2 |
| #3166 | 139 |