Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
268 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 69 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. C16×D356 | C2 | semidirect |
| 2. #26019604 | C2 | semidirect |
| 3. #26018324 | C2 | semidirect |
| 4. #26018298 | C2 | semidirect |
| 5. C89×#2246 | C2 | semidirect |
| 54. C16×C89 | D8 | semidirect |
| 67. D356 | D16 | semidirect |
| 94. #2246 | D89 | semidirect |
| 99. C89 | #12430 | semidirect |
| 148. C16 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D356 | 2 |
| #26019604 | 2 |
| #26018324 | 2 |
| #26018298 | 2 |
| C89×#2246 | 2 |
| #12430 | 89 |