Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
232 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22580993 | C2 | semidirect |
| 5. #22580911 | C2 | semidirect |
| 6. #22580717 | C2 | semidirect |
| 7. #343×C139 | C2 | semidirect |
| 18. #17984758 | C4 | semidirect |
| 100. C139 | #1931 | semidirect |
| 107. #343 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22580993 | 2 |
| #22580959 | 2 |
| C2×#17984762 | 2 |
| C2×#17984758 | 2 |
| #22580911 | 2 |
| #22580717 | 2 |
| #343×C139 | 2 |
| #1931 | 139 |