Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26021242 | C2 | semidirect |
| 3. #26019008 | C2 | semidirect |
| 4. #26018933 | C2 | semidirect |
| 6. C8×#13083558 | C2 | semidirect |
| 64. #13083558 | SD16 | semidirect |
| 127. C8×C89 | #100 | semidirect |
| 161. C89 | #9793 | semidirect |
| 285. C8 | #15667929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021242 | 2 |
| #26021093 | 2 |
| #26019008 | 2 |
| #26018933 | 2 |
| #26018920 | 2 |
| C8×#13083558 | 2 |
| C2×#492×C89 | 2 |
| #9793 | 89 |