Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
278 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22580996 | C2 | semidirect |
| 4. C2×#17984761 | C2 | semidirect |
| 5. #22580860 | C2 | semidirect |
| 6. #22580712 | C2 | semidirect |
| 120. C139 | #2038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22580996 | 2 |
| C2×#17984769 | 2 |
| #22580954 | 2 |
| C2×#17984761 | 2 |
| #22580860 | 2 |
| #22580712 | 2 |
| #536×C139 | 2 |
| #2038 | 139 |