Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. #14530585 | C2 | semidirect |
| 3. #14527538 | C2 | semidirect |
| 4. #14526754 | C2 | semidirect |
| 5. #14526752 | C2 | semidirect |
| 6. #14526750 | C2 | semidirect |
| 7. C17×#1334 | C2 | semidirect |
| 74. Q16×C17 | M16 | semidirect |
| 97. D136 | M16 | semidirect |
| 139. #1334 | D17 | semidirect |
| 218. C17 | #11666 | semidirect |
| 231. Q16 | #63218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587605 | 2 |
| #14530585 | 2 |
| #14527538 | 2 |
| #14526754 | 2 |
| #14526752 | 2 |
| #14526750 | 2 |
| C17×#1334 | 2 |
| #11666 | 17 |