Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #26021972 | C2 | semidirect |
| 4. #26021124 | C2 | semidirect |
| 5. #26018358 | C2 | semidirect |
| 6. #26018335 | C2 | semidirect |
| 24. #510×C89 | C4 | semidirect |
| 61. C2×Q16×C89 | C2×C4 | semidirect |
| 69. M32×C89 | C2×C4 | semidirect |
| 184. C89 | #13026 | semidirect |
| 189. #510 | Dic89 | semidirect |
| 216. C2×Q16 | C2×Dic89 | semidirect |
| 235. M32 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029053 | 2 |
| C2×#19151408 | 2 |
| #26021972 | 2 |
| #26021124 | 2 |
| #26018358 | 2 |
| #26018335 | 2 |
| C2×#510×C89 | 2 |
| #13026 | 89 |