Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
166 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 4. #22580704 | C2 | semidirect |
| 5. #22580702 | C2 | semidirect |
| 6. #22580699 | C2 | semidirect |
| 7. #498×C139 | C2 | semidirect |
| 59. C8×C139 | SD16 | semidirect |
| 76. C139 | #1671 | semidirect |
| 78. #498 | D139 | semidirect |
| 136. C8 | #14555772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581240 | 2 |
| #22581155 | 2 |
| C8×D556 | 2 |
| #22580704 | 2 |
| #22580702 | 2 |
| #22580699 | 2 |
| #498×C139 | 2 |
| #1671 | 139 |