Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
580 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26020532 | C2 | semidirect |
| 4. #26018370 | C2 | semidirect |
| 11. #19151391 | C4 | semidirect |
| 29. #15667927 | C2×C4 | semidirect |
| 72. C2×D4×C89 | C4⋊C4 | semidirect |
| 89. C42×C89 | C4⋊C4 | semidirect |
| 167. C89 | #12966 | semidirect |
| 221. C2×D4 | #13083553 | semidirect |
| 251. C42 | #13083553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| #26020651 | 2 |
| #26020532 | 2 |
| #26018370 | 2 |
| C89×#2380 | 2 |
| #12966 | 89 |