Finite Group DatabasebetaFinite Group DatabasebetaOrder 28544.
202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. #28383335 | C2 | semidirect |
| 15. C2×D4×C223 | C8 | semidirect |
| 63. C223 | #1270 | semidirect |
| 76. C2×D4 | C223⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28383335 | 2 |
| #390×C223 | 2 |
| #1270 | 223 |