Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 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. #14541920 | C2 | semidirect |
| 2. C2×#11763247 | C2 | semidirect |
| 3. #14539270 | C2 | semidirect |
| 4. #14530521 | C2 | semidirect |
| 5. #14530501 | C2 | semidirect |
| 6. #14529682 | C2 | semidirect |
| 7. C17×#1378 | C2 | semidirect |
| 43. C2×Dic68 | D4 | semidirect |
| 60. C2×D136 | D4 | semidirect |
| 71. C17×M32 | D4 | semidirect |
| 73. C2×C16×C17 | D4 | semidirect |
| 197. #1378 | D17 | semidirect |
| 294. M32 | D68 | semidirect |
| 296. C2×C16 | D68 | semidirect |
| 303. C17 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541920 | 2 |
| C2×#11763247 | 2 |
| #14539270 | 2 |
| #14530521 | 2 |
| #14530501 | 2 |
| #14529682 | 2 |
| C17×#1378 | 2 |
| #13334 | 17 |