Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
572 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 101 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×#10587497 | C2 | semidirect |
| 2. C2×#11763079 | C2 | semidirect |
| 3. C2×#11762622 | C2 | semidirect |
| 4. #14530499 | C2 | semidirect |
| 5. C2×#11762593 | C2 | semidirect |
| 6. #14526879 | C2 | semidirect |
| 7. C17×#3058 | C2 | semidirect |
| 61. C2×D136 | D4 | semidirect |
| 68. #10587490 | D4 | semidirect |
| 74. C2×#63214 | D4 | semidirect |
| 175. #3058 | D17 | semidirect |
| 274. C17 | #13319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587497 | 2 |
| C2×#11763079 | 2 |
| C2×#11762622 | 2 |
| #14530499 | 2 |
| C2×#11762593 | 2 |
| #14526879 | 2 |
| C17×#3058 | 2 |
| #13319 | 17 |