Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
662 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26030339 | C2 | semidirect |
| 2. #26026105 | C2 | semidirect |
| 3. #26018876 | C2 | semidirect |
| 4. #26018799 | C2 | semidirect |
| 5. #26018696 | C2 | semidirect |
| 6. #26018117 | C2 | semidirect |
| 7. C89×#3153 | C2 | semidirect |
| 53. #15667923 | D4 | semidirect |
| 68. C4⋊Q8×C89 | D4 | semidirect |
| 69. #127×C89 | D4 | semidirect |
| 83. C4×C8×C89 | D4 | semidirect |
| 228. #3153 | D89 | semidirect |
| 235. C89 | #10018 | semidirect |
| 275. C4⋊Q8 | C22⋊D89 | semidirect |
| 276. #127 | C22⋊D89 | semidirect |
| 307. C4×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030339 | 2 |
| #26026105 | 2 |
| #26018876 | 2 |
| #26018799 | 2 |
| #26018696 | 2 |
| #26018117 | 2 |
| C89×#3153 | 2 |
| #10018 | 89 |