Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
570 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 270 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×#63216 | C2 | semidirect |
| 2. #14545163 | C2 | semidirect |
| 3. #14545143 | C2 | semidirect |
| 4. #14545114 | C2 | semidirect |
| 39. #63256 | C16 | semidirect |
| 62. Q8×C17 | C2×C16 | semidirect |
| 69. D68 | C2×C16 | semidirect |
| 73. C4×D17 | C2×C16 | semidirect |
| 131. C17 | #33502 | semidirect |
| 155. Q8 | #10587529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#63216 | 2 |
| #14545163 | 2 |
| #14545143 | 2 |
| #14545114 | 2 |
| C8×#63256 | 2 |
| #33502 | 17 |