Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#19152036 | C2 | semidirect |
| 2. #26029973 | C2 | semidirect |
| 3. #26029901 | C2 | semidirect |
| 4. C2×#19151410 | C2 | semidirect |
| 5. #26021987 | C2 | semidirect |
| 6. #26021881 | C2 | semidirect |
| 7. C89×#1389 | C2 | semidirect |
| 43. C2×Dic356 | D4 | semidirect |
| 51. C2×D712 | D4 | semidirect |
| 75. M32×C89 | D4 | semidirect |
| 78. #108×C89 | D4 | semidirect |
| 218. #1389 | D89 | semidirect |
| 219. C89 | #13310 | semidirect |
| 283. M32 | D356 | semidirect |
| 287. #108 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152036 | 2 |
| #26029973 | 2 |
| #26029901 | 2 |
| C2×#19151410 | 2 |
| #26021987 | 2 |
| #26021881 | 2 |
| C89×#1389 | 2 |
| #13310 | 89 |