Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
252 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 93 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. D4×#63214 | C2 | semidirect |
| 2. #14530603 | C2 | semidirect |
| 4. #14526847 | C2 | semidirect |
| 5. #14526740 | C2 | semidirect |
| 6. #14526703 | C2 | semidirect |
| 7. C17×D4⋊C16 | C2 | semidirect |
| 57. #63228 | C16 | semidirect |
| 75. D4×C17 | C2×C16 | semidirect |
| 84. D68 | C2×C16 | semidirect |
| 94. #3622 | C2×C16 | semidirect |
| 100. D4⋊C16 | D17 | semidirect |
| 158. C17 | #12062 | semidirect |
| 190. D4 | C16×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#63214 | 2 |
| #14530603 | 2 |
| C8×#63228 | 2 |
| #14526847 | 2 |
| #14526740 | 2 |
| #14526703 | 2 |
| C17×D4⋊C16 | 2 |
| #12062 | 17 |