Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
238 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 81 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. Q8×#63241 | C2 | semidirect |
| 3. #14545843 | C2 | semidirect |
| 4. Q8⋊#63241 | C2 | semidirect |
| 6. C8×#63241 | C2 | semidirect |
| 58. #63241 | SD16 | semidirect |
| 61. #63230 | C16 | semidirect |
| 71. Q8×C17 | C2×C16 | semidirect |
| 89. #3622 | C2×C16 | semidirect |
| 149. C17 | C16×SD16 | semidirect |
| 176. Q8 | #10587665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#63241 | 2 |
| #14545993 | 2 |
| #14545843 | 2 |
| Q8⋊#63241 | 2 |
| #14545827 | 2 |
| C8×#63241 | 2 |
| #14544368 | 2 |
| C16×SD16 | 17 |