Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
242 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 87 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. #14530617 | C2 | semidirect |
| 3. #14526847 | C2 | semidirect |
| 4. D4⋊#63214 | C2 | semidirect |
| 5. #14526738 | C2 | semidirect |
| 6. #14526703 | C2 | semidirect |
| 7. D4×C16×C17 | C2 | semidirect |
| 75. D4×C17 | M32 | semidirect |
| 96. D4×C16 | D17 | semidirect |
| 158. C17 | #12063 | semidirect |
| 190. D4 | #10587469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14530617 | 2 |
| C8×#63228 | 2 |
| #14526847 | 2 |
| D4⋊#63214 | 2 |
| #14526738 | 2 |
| #14526703 | 2 |
| D4×C16×C17 | 2 |
| #12063 | 17 |