Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
384 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 79 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. #14531041 | C2 | semidirect |
| 2. #14530824 | C2 | semidirect |
| 4. #14526833 | C2 | semidirect |
| 5. #14526748 | C2 | semidirect |
| 6. D4⋊#63214 | C2 | semidirect |
| 7. D4×Q16×C17 | C2 | semidirect |
| 72. Q16×C17 | D8 | semidirect |
| 104. D4×C17 | SD32 | semidirect |
| 125. D4×Q16 | D17 | semidirect |
| 201. C17 | #12318 | semidirect |
| 218. Q16 | #63228 | semidirect |
| 254. D4 | #10587499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14531041 | 2 |
| #14530824 | 2 |
| #14528139 | 2 |
| #14526833 | 2 |
| #14526748 | 2 |
| D4⋊#63214 | 2 |
| D4×Q16×C17 | 2 |
| #12318 | 17 |