Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
686 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26030248 | C2 | semidirect |
| 2. #26029712 | C2 | semidirect |
| 3. #26025154 | C2 | semidirect |
| 4. #26018678 | C2 | semidirect |
| 5. #26018642 | C2 | semidirect |
| 6. #26018110 | C2 | semidirect |
| 7. C89×#1517 | C2 | semidirect |
| 63. C4⋊#10623494 | D4 | semidirect |
| 69. C4×#10623494 | D4 | semidirect |
| 72. C4⋊Q8×C89 | D4 | semidirect |
| 73. #127×C89 | D4 | semidirect |
| 99. C2×D356 | D8 | semidirect |
| 260. #1517 | D89 | semidirect |
| 264. C89 | #9996 | semidirect |
| 302. C4⋊Q8 | D356 | semidirect |
| 303. #127 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030248 | 2 |
| #26029712 | 2 |
| #26025154 | 2 |
| #26018678 | 2 |
| #26018642 | 2 |
| #26018110 | 2 |
| C89×#1517 | 2 |
| #9996 | 89 |