Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1422 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 263 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 |
|---|---|---|
| 2. C22×#3754 | C2 | semidirect |
| 3. C2×#63659 | C2 | semidirect |
| 4. #10592628 | C2 | semidirect |
| 5. #10589390 | C2 | semidirect |
| 41. C2×#634 | D4 | semidirect |
| 47. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 74. C2×C32×C4 | SD16 | semidirect |
| 156. C2×C3×C4 | #214 | semidirect |
| 214. C32 | #2014 | semidirect |
| 235. C2×C4 | #3754 | semidirect |
| 262. C3 | #71768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#127 | 2 |
| C22×#3754 | 2 |
| C2×#63659 | 2 |
| #10592628 | 2 |
| #10589390 | 2 |
| #71768 | 3 |