Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
542 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 3. M16×#3624 | C2 | semidirect |
| 4. #14543630 | C2 | semidirect |
| 43. C17×#100 | C8 | semidirect |
| 44. #10587504 | C8 | semidirect |
| 71. M16×C17 | C2×C8 | semidirect |
| 78. #63223 | C2×C8 | semidirect |
| 108. #3624 | #100 | direct (N × H) |
| 172. #100 | #3624 | direct (N × H) |
| 180. C17 | C8×#100 | semidirect |
| 197. M16 | C2×#3624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#3624 | 2 |
| #14544024 | 2 |
| M16×#3624 | 2 |
| #14543630 | 2 |
| #100×Dic17 | 2 |
| C8×#100 | 17 |