Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1502 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 331 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×#11763203 | C2 | semidirect |
| 2. C2×#11763198 | C2 | semidirect |
| 3. C2×#11763193 | C2 | semidirect |
| 4. C2×#11763182 | C2 | semidirect |
| 5. #14534894 | C2 | semidirect |
| 6. #14534890 | C2 | semidirect |
| 7. C17×#1726 | C2 | semidirect |
| 55. C17×#97 | D4 | semidirect |
| 56. C4×C8×C17 | D4 | semidirect |
| 124. #1726 | D17 | semidirect |
| 188. #97 | D68 | semidirect |
| 189. C4×C8 | D68 | semidirect |
| 191. C17 | #33307 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763203 | 2 |
| C2×#11763198 | 2 |
| C2×#11763193 | 2 |
| C2×#11763182 | 2 |
| #14534894 | 2 |
| #14534890 | 2 |
| C17×#1726 | 2 |
| #33307 | 17 |