Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 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. D8×#3624 | C2 | semidirect |
| 2. #14543815 | C2 | semidirect |
| 3. #14543738 | C2 | semidirect |
| 4. C16×#3624 | C2 | semidirect |
| 24. C17×D16 | C8 | semidirect |
| 38. D8×C17 | C2×C8 | semidirect |
| 45. C16×C17 | C2×C8 | semidirect |
| 60. #3624 | D16 | direct (N × H) |
| 96. D16 | #3624 | direct (N × H) |
| 107. C17 | C8×D16 | semidirect |
| 111. D8 | C2×#3624 | semidirect |
| 124. C16 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#3624 | 2 |
| #14543815 | 2 |
| #14543738 | 2 |
| C16×#3624 | 2 |
| D16×Dic17 | 2 |
| C8×D16 | 17 |