Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
632 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26030261 | C2 | semidirect |
| 2. #26030051 | C2 | semidirect |
| 4. #26018815 | C2 | semidirect |
| 5. #26018676 | C2 | semidirect |
| 6. #26018644 | C2 | semidirect |
| 7. C89×#1286 | C2 | semidirect |
| 39. #15668012 | D4 | semidirect |
| 40. #15668012 | D4 | semidirect |
| 79. C4⋊C8×C89 | D4 | semidirect |
| 81. C4×C8×C89 | D4 | semidirect |
| 99. C2×D356 | SD16 | semidirect |
| 244. #1286 | D89 | semidirect |
| 245. C89 | #10000 | semidirect |
| 310. C4⋊C8 | D356 | semidirect |
| 318. C4×C8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030261 | 2 |
| #26030051 | 2 |
| #26025154 | 2 |
| #26018815 | 2 |
| #26018676 | 2 |
| #26018644 | 2 |
| C89×#1286 | 2 |
| #10000 | 89 |