Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26031167 | C2 | semidirect |
| 2. #26029712 | C2 | semidirect |
| 3. #26025194 | C2 | semidirect |
| 4. #26018919 | C2 | semidirect |
| 5. #26018644 | C2 | semidirect |
| 6. #26018155 | C2 | semidirect |
| 7. C89×#1502 | C2 | semidirect |
| 58. C4⋊#10623494 | D4 | semidirect |
| 59. C4⋊#10623494 | D4 | semidirect |
| 66. C4⋊Q8×C89 | D4 | semidirect |
| 67. #127×C89 | D4 | semidirect |
| 102. C2×D356 | D8 | semidirect |
| 245. #1502 | D89 | semidirect |
| 248. C89 | #10238 | semidirect |
| 285. C4⋊Q8 | D356 | semidirect |
| 292. #127 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031167 | 2 |
| #26029712 | 2 |
| #26025194 | 2 |
| #26018919 | 2 |
| #26018644 | 2 |
| #26018155 | 2 |
| C89×#1502 | 2 |
| #10238 | 89 |