Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
828 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 131 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×#11763001 | C2 | semidirect |
| 2. #14533700 | C2 | semidirect |
| 3. C2×#11762538 | C2 | semidirect |
| 4. #14526667 | C2 | semidirect |
| 5. C17×#1957 | C2 | semidirect |
| 28. C17×#127 | D4 | semidirect |
| 50. C4⋊#3622 | D4 | semidirect |
| 74. C2×D68 | D8 | semidirect |
| 147. #1957 | D17 | semidirect |
| 208. #127 | D68 | semidirect |
| 227. C17 | #10228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763001 | 2 |
| #14533700 | 2 |
| C2×#11762538 | 2 |
| #14526667 | 2 |
| C17×#1957 | 2 |
| #10228 | 17 |