Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
449 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 449 conjugacy classes of subgroups — too many to draw. Only its 168 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. #10589100 | C2 | semidirect |
| 59. C3⋊(C3⋊C8) | M16 | semidirect |
| 173. C32 | #1567 | semidirect |
| 208. C3 | #70491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C3×#4924 | 2 |
| #10589100 | 2 |
| #70491 | 3 |