Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26022053 | C2 | semidirect |
| 3. #26019006 | C2 | semidirect |
| 4. #26018222 | C2 | semidirect |
| 5. #26018220 | C2 | semidirect |
| 6. #26018218 | C2 | semidirect |
| 7. C89×#1334 | C2 | semidirect |
| 74. D712 | M16 | semidirect |
| 95. Q16×C89 | M16 | semidirect |
| 161. #1334 | D89 | semidirect |
| 164. C89 | #11666 | semidirect |
| 231. Q16 | #13083557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668035 | 2 |
| #26022053 | 2 |
| #26019006 | 2 |
| #26018222 | 2 |
| #26018220 | 2 |
| #26018218 | 2 |
| C89×#1334 | 2 |
| #11666 | 89 |