Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
632 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 101 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. #14538792 | C2 | semidirect |
| 2. #14538581 | C2 | semidirect |
| 3. #14527347 | C2 | semidirect |
| 4. #14527209 | C2 | semidirect |
| 5. #14527175 | C2 | semidirect |
| 6. #14526642 | C2 | semidirect |
| 62. #10587555 | D4 | semidirect |
| 63. #10587555 | D4 | semidirect |
| 81. C4⋊#3622 | D4 | semidirect |
| 83. C4×#3622 | D4 | semidirect |
| 97. C2×D4×C17 | SD16 | semidirect |
| 321. C17 | #10000 | semidirect |
| 337. C2×D4 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14538792 | 2 |
| #14538581 | 2 |
| #14527347 | 2 |
| #14527209 | 2 |
| #14527175 | 2 |
| #14526642 | 2 |
| C17×#2535 | 2 |
| #10000 | 17 |