Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
944 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#11762948 | C2 | semidirect |
| 3. C2×#11762542 | C2 | semidirect |
| 4. #14526627 | C2 | semidirect |
| 5. C17×#1446 | C2 | semidirect |
| 24. C22×Q8×C17 | D4 | semidirect |
| 50. C22⋊#3622 | D4 | semidirect |
| 75. C22×C4×C17 | SD16 | semidirect |
| 150. #1446 | D17 | semidirect |
| 206. C22×Q8 | D68 | semidirect |
| 233. C17 | #9964 | semidirect |
| 269. C22×C4 | #63230 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11762948 | 2 |
| #14534886 | 2 |
| C2×#11762542 | 2 |
| #14526627 | 2 |
| C17×#1446 | 2 |
| #9964 | 17 |