Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
470 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 118 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. C4×#10587529 | C2 | semidirect |
| 2. #14544329 | C2 | semidirect |
| 3. #14543739 | C2 | semidirect |
| 4. #14543738 | C2 | semidirect |
| 8. #11763695 | C22 | semidirect |
| 11. #11763672 | C22 | semidirect |
| 32. D8×D17 | C8 | semidirect |
| 76. D8×C17 | C2×C8 | semidirect |
| 94. D136 | C2×C8 | semidirect |
| 185. D17 | #1331 | semidirect |
| 220. C17 | C2×#1331 | semidirect |
| 241. D8 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587529 | 2 |
| #14544329 | 2 |
| #14543739 | 2 |
| #14543738 | 2 |
| C4×D8×D17 | 2 |
| C2×#1331 | 17 |