Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
770 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26031235 | C2 | semidirect |
| 2. #26030705 | C2 | semidirect |
| 3. #26026358 | C2 | semidirect |
| 4. #26018965 | C2 | semidirect |
| 5. #26018851 | C2 | semidirect |
| 6. #26018145 | C2 | semidirect |
| 7. C89×#1505 | C2 | semidirect |
| 56. C4⋊#10623494 | D4 | semidirect |
| 61. #15667923 | D4 | semidirect |
| 64. C4⋊Q8×C89 | D4 | semidirect |
| 65. #127×C89 | D4 | semidirect |
| 217. #1505 | D89 | semidirect |
| 219. C89 | #10088 | semidirect |
| 256. C4⋊Q8 | D356 | semidirect |
| 262. #127 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031235 | 2 |
| #26030705 | 2 |
| #26026358 | 2 |
| #26018965 | 2 |
| #26018851 | 2 |
| #26018145 | 2 |
| C89×#1505 | 2 |
| #10088 | 89 |