Finite Group DatabasebetaFinite Group DatabasebetaOrder 28544.
126 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 41 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. C22⋊(C223⋊C16) | C2 | semidirect |
| 2. #28383343 | C2 | semidirect |
| 6. C2×D8×C223 | C4 | semidirect |
| 9. #107×C223 | C4 | semidirect |
| 59. C223 | #1347 | semidirect |
| 64. C2×D8 | Dic223 | semidirect |
| 69. #107 | Dic223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊(C223⋊C16) | 2 |
| #28383343 | 2 |
| #466×C223 | 2 |
| #1347 | 223 |