Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
662 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 662 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. #14545163 | C2 | semidirect |
| 2. #14545141 | C2 | semidirect |
| 3. #14545009 | C2 | semidirect |
| 5. C2×#10587529 | C22 | semidirect |
| 6. C4⋊#63216 | C22 | semidirect |
| 7. #11763704 | C22 | semidirect |
| 9. C4×#63216 | C22 | semidirect |
| 41. C2×D68 | C16 | semidirect |
| 65. C22×D17 | C2×C16 | semidirect |
| 70. C2×C4×C17 | C2×C16 | semidirect |
| 77. D68 | C2×C16 | semidirect |
| 139. C17 | #33486 | semidirect |
| 179. C2×C4 | #10587529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545163 | 2 |
| #14545141 | 2 |
| #14545009 | 2 |
| C2×#11762874 | 2 |
| #33486 | 17 |