Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
| 98. Q8×C17 | C2×C16 | semidirect |
| 101. D4×C17 | C2×C16 | semidirect |
| 204. C17 | #11621 | semidirect |
| 206. #41 | #63241 | semidirect |
| 247. Q8 | C2×#63241 | semidirect |
| 250. 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 |
| #11621 | 17 |