Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
520 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 100 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. #14545591 | C2 | semidirect |
| 2. #14544081 | C2 | semidirect |
| 3. C2×#11763657 | C2 | semidirect |
| 4. #14544025 | C2 | semidirect |
| 5. #14543630 | C2 | semidirect |
| 6. #14543617 | C2 | semidirect |
| 99. C2×D68 | M16 | semidirect |
| 117. M16×C17 | M16 | semidirect |
| 308. C17 | #9097 | semidirect |
| 340. M16 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545591 | 2 |
| #14544081 | 2 |
| C2×#11763657 | 2 |
| #14544025 | 2 |
| #14543630 | 2 |
| #14543617 | 2 |
| #14537591 | 2 |
| #9097 | 17 |