Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 254 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. C8×D712 | C2 | semidirect |
| 3. #26018325 | C2 | semidirect |
| 4. #26018213 | C2 | semidirect |
| 5. #26018212 | C2 | semidirect |
| 6. #26018169 | C2 | semidirect |
| 7. C8×D8×C89 | C2 | semidirect |
| 26. #15667953 | C8 | semidirect |
| 47. D712 | C2×C8 | semidirect |
| 54. #13083549 | C2×C8 | semidirect |
| 58. D8×C89 | C2×C8 | semidirect |
| 114. C8×D8 | D89 | semidirect |
| 119. C89 | #12045 | semidirect |
| 163. D8 | C8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667953 | 2 |
| C8×D712 | 2 |
| #26018325 | 2 |
| #26018213 | 2 |
| #26018212 | 2 |
| #26018169 | 2 |
| C8×D8×C89 | 2 |
| #12045 | 89 |