Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#10587499 | C2 | semidirect |
| 2. C2×#11763081 | C2 | semidirect |
| 4. C2×#11762623 | C2 | semidirect |
| 5. C2×#11762594 | C2 | semidirect |
| 6. #14526879 | C2 | semidirect |
| 7. C17×#2141 | C2 | semidirect |
| 37. C2×Q16×C17 | D4 | semidirect |
| 70. #10587490 | D4 | semidirect |
| 73. C2×#63214 | D4 | semidirect |
| 176. #2141 | D17 | semidirect |
| 234. C2×Q16 | D68 | semidirect |
| 269. C17 | #13321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587499 | 2 |
| C2×#11763081 | 2 |
| #14538433 | 2 |
| C2×#11762623 | 2 |
| C2×#11762594 | 2 |
| #14526879 | 2 |
| C17×#2141 | 2 |
| #13321 | 17 |