Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
740 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 105 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. #14539725 | C2 | semidirect |
| 2. #14538581 | C2 | semidirect |
| 3. #14527452 | C2 | semidirect |
| 4. #14527282 | C2 | semidirect |
| 5. #14527175 | C2 | semidirect |
| 6. #14526687 | C2 | semidirect |
| 60. #10587555 | D4 | semidirect |
| 61. #10587555 | D4 | semidirect |
| 74. C4⋊#3622 | D4 | semidirect |
| 75. C4⋊#3622 | D4 | semidirect |
| 100. C2×D4×C17 | SD16 | semidirect |
| 299. C17 | #10246 | semidirect |
| 324. C2×D4 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539725 | 2 |
| #14538581 | 2 |
| #14527452 | 2 |
| #14527282 | 2 |
| #14527175 | 2 |
| #14526687 | 2 |
| C17×#2541 | 2 |
| #10246 | 17 |