Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
612 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 161 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. C32×C8×D4 | C2 | semidirect |
| 2. #10592714 | C2 | semidirect |
| 3. #10592394 | C2 | semidirect |
| 4. #10589351 | C2 | semidirect |
| 5. #10589324 | C2 | semidirect |
| 18. C3×C8×D4 | D3 | semidirect |
| 54. C32×D4 | D8 | semidirect |
| 68. C32×C8 | D8 | semidirect |
| 72. C8×D4 | C3⋊D3 | semidirect |
| 118. C3×D4 | D24 | semidirect |
| 132. C3×C8 | #213 | semidirect |
| 168. C32 | #1667 | semidirect |
| 177. D4 | #3745 | semidirect |
| 187. C8 | #3753 | semidirect |
| 206. C3 | #70847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×D4 | 2 |
| #10592714 | 2 |
| #10592394 | 2 |
| #10589351 | 2 |
| #10589324 | 2 |
| #70847 | 3 |