Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
242 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26018325 | C2 | semidirect |
| 4. #26018216 | C2 | semidirect |
| 6. C8×#13083549 | C2 | semidirect |
| 7. C8×Q16×C89 | C2 | semidirect |
| 26. #15667955 | C8 | direct (N × H) |
| 54. #13083549 | C2×C8 | semidirect |
| 57. Q16×C89 | C2×C8 | semidirect |
| 85. C8×C89 | SD32 | semidirect |
| 107. C8×Q16 | D89 | semidirect |
| 113. C89 | C8×SD32 | semidirect |
| 154. Q16 | C8×D89 | semidirect |
| 192. C8 | #15667955 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667955 | 2 |
| C8×D712 | 2 |
| #26018325 | 2 |
| #26018216 | 2 |
| #26018212 | 2 |
| C8×#13083549 | 2 |
| C8×Q16×C89 | 2 |
| C8×SD32 | 89 |