Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
238 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 74 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. #14544372 | C2 | semidirect |
| 3. #14543816 | C2 | semidirect |
| 4. #14543741 | C2 | semidirect |
| 6. #14543695 | C2 | semidirect |
| 39. #10587498 | C8 | semidirect |
| 64. Dic68 | C2×C8 | semidirect |
| 67. #63214 | C2×C8 | semidirect |
| 149. C17 | #12043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544372 | 2 |
| D8×#3624 | 2 |
| #14543816 | 2 |
| #14543741 | 2 |
| #14543738 | 2 |
| #14543695 | 2 |
| #14530639 | 2 |
| #12043 | 17 |