Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22581323 | C2 | semidirect |
| 4. #22581322 | C2 | semidirect |
| 5. #22581321 | C2 | semidirect |
| 6. #22581302 | C2 | semidirect |
| 9. #491×C139 | C2 | semidirect |
| 87. C139 | #3139 | semidirect |
| 94. #491 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581509 | 2 |
| C4⋊Q8×D139 | 2 |
| #22581323 | 2 |
| #22581322 | 2 |
| #22581321 | 2 |
| #22581302 | 2 |
| #22580960 | 2 |
| #22580905 | 2 |
| #491×C139 | 2 |
| #3139 | 139 |