Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
454 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 134 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. C2×C22⋊#63216 | C2 | semidirect |
| 2. #14543720 | C2 | semidirect |
| 3. #14543704 | C2 | semidirect |
| 47. C2×D4×C17 | C16 | semidirect |
| 89. C23×C17 | C2×C16 | semidirect |
| 109. C2×C4×C17 | C2×C16 | semidirect |
| 188. C17 | #11465 | semidirect |
| 193. C2×D4 | #63216 | semidirect |
| 233. C23 | C2×#63216 | semidirect |
| 253. C2×C4 | C2×#63216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#63216 | 2 |
| #14543720 | 2 |
| #14543704 | 2 |
| C2×D4×#3622 | 2 |
| #11465 | 17 |