Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
456 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22581057 | C2 | semidirect |
| 5. #22581045 | C2 | semidirect |
| 11. C2×#14555775 | C4 | semidirect |
| 98. C139 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555775 | 2 |
| #22581431 | 2 |
| #22581430 | 2 |
| #22581057 | 2 |
| #22581045 | 2 |
| #22580989 | 2 |
| #22580963 | 2 |
| #22580911 | 2 |
| #419×C139 | 2 |
| #2950 | 139 |