Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
254 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 82 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. #14543817 | C2 | semidirect |
| 3. #14543738 | C2 | semidirect |
| 4. #14543695 | C2 | semidirect |
| 24. C17×D16 | C8 | semidirect |
| 37. D8×C17 | C2×C8 | semidirect |
| 44. C16×C17 | C2×C8 | semidirect |
| 93. D16 | #3624 | semidirect |
| 104. C17 | #12045 | semidirect |
| 108. D8 | C2×#3624 | semidirect |
| 120. 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 |
| #14543817 | 2 |
| #14543738 | 2 |
| #14543695 | 2 |
| D16×Dic17 | 2 |
| #12045 | 17 |