Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
284 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 132 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. #14543697 | C2 | semidirect |
| 4. #14543697 | C2 | semidirect |
| 5. #14543696 | C2 | semidirect |
| 6. C8×#63216 | C2 | semidirect |
| 64. #63216 | M16 | semidirect |
| 80. C8×C17 | M32 | semidirect |
| 142. C17 | #11409 | semidirect |
| 183. C8 | #10587530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545143 | 2 |
| C4×#10587530 | 2 |
| #14543697 | 2 |
| #14543696 | 2 |
| C8×#63216 | 2 |
| #14527063 | 2 |
| #11409 | 17 |