Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
224 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 66 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. Q16×#3624 | C2 | semidirect |
| 3. #14543815 | C2 | semidirect |
| 4. #14543740 | C2 | semidirect |
| 6. #14543698 | C2 | semidirect |
| 54. Q16×C17 | M16 | semidirect |
| 149. C17 | #12075 | semidirect |
| 154. Q16 | #63243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544416 | 2 |
| Q16×#3624 | 2 |
| #14543815 | 2 |
| #14543740 | 2 |
| #14543739 | 2 |
| #14543698 | 2 |
| #14530633 | 2 |
| #12075 | 17 |