Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
828 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 137 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×#11763004 | C2 | semidirect |
| 2. #14529589 | C2 | semidirect |
| 3. C2×D4⋊#3622 | C2 | semidirect |
| 4. #14526667 | C2 | semidirect |
| 5. C17×#2537 | C2 | semidirect |
| 44. #10587560 | D4 | semidirect |
| 49. C4⋊#3622 | D4 | semidirect |
| 60. C2×D4×C17 | D8 | semidirect |
| 146. #2537 | D17 | semidirect |
| 227. C17 | #10228 | semidirect |
| 247. C2×D4 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763004 | 2 |
| #14529589 | 2 |
| C2×D4⋊#3622 | 2 |
| #14526667 | 2 |
| C17×#2537 | 2 |
| #10228 | 17 |