Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
402 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 102 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. #14544991 | C2 | semidirect |
| 2. #14544329 | C2 | semidirect |
| 3. #14543740 | C2 | semidirect |
| 4. #14543739 | C2 | semidirect |
| 30. #10587605 | C8 | semidirect |
| 71. Q16×C17 | C2×C8 | semidirect |
| 92. D136 | C2×C8 | semidirect |
| 208. C17 | #11592 | semidirect |
| 221. Q16 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544991 | 2 |
| #14544329 | 2 |
| #14543740 | 2 |
| #14543739 | 2 |
| C4×#10587605 | 2 |
| #11592 | 17 |