Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C4×C16×D89 | C2 | semidirect |
| 3. #26018999 | C2 | semidirect |
| 4. #26018216 | C2 | semidirect |
| 5. #26018214 | C2 | semidirect |
| 6. #26018212 | C2 | semidirect |
| 7. C89×#1332 | C2 | semidirect |
| 29. #15668035 | C8 | semidirect |
| 164. #1332 | D89 | semidirect |
| 167. C89 | #11591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668035 | 2 |
| C4×C16×D89 | 2 |
| #26018999 | 2 |
| #26018216 | 2 |
| #26018214 | 2 |
| #26018212 | 2 |
| C89×#1332 | 2 |
| #11591 | 89 |