Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
560 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26029280 | C2 | semidirect |
| 3. C4×#15667928 | C2 | semidirect |
| 4. #26018851 | C2 | semidirect |
| 5. #26018849 | C2 | semidirect |
| 6. #26018116 | C2 | semidirect |
| 7. C89×#1288 | C2 | semidirect |
| 64. #15667923 | D4 | semidirect |
| 73. #97×C89 | D4 | semidirect |
| 245. #1288 | D89 | semidirect |
| 246. C89 | #9187 | semidirect |
| 309. #97 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029280 | 2 |
| #26026107 | 2 |
| C4×#15667928 | 2 |
| #26018851 | 2 |
| #26018849 | 2 |
| #26018116 | 2 |
| C89×#1288 | 2 |
| #9187 | 89 |