Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
378 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14545981 | C2 | semidirect |
| 2. C2×C4×#63241 | C2 | semidirect |
| 3. Q8⋊#63241 | C2 | semidirect |
| 4. D4⋊#63241 | C2 | semidirect |
| 56. #41×C17 | C16 | semidirect |
| 96. Q8×C17 | C2×C16 | semidirect |
| 99. D4×C17 | C2×C16 | semidirect |
| 201. C17 | #11613 | semidirect |
| 203. #41 | #63241 | semidirect |
| 242. Q8 | C2×#63241 | semidirect |
| 245. D4 | C2×#63241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545981 | 2 |
| C2×C4×#63241 | 2 |
| Q8⋊#63241 | 2 |
| D4⋊#63241 | 2 |
| #41×#3624 | 2 |
| #11613 | 17 |