Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1212 conjugacy classes of subgroups; only the 321 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 321 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. #10596041 | C2 | semidirect |
| 3. C32×C8×Q8 | C2 | semidirect |
| 4. #10592547 | C2 | semidirect |
| 5. #10592540 | C2 | semidirect |
| 6. #10592392 | C2 | semidirect |
| 7. C4×#3744 | C2 | semidirect |
| 27. C3×C8×Q8 | D3 | semidirect |
| 70. C32×Q8 | SD16 | semidirect |
| 85. C32×C8 | #41 | semidirect |
| 91. C8×Q8 | C3⋊D3 | semidirect |
| 141. C3×Q8 | #204 | semidirect |
| 156. C3×C8 | #239 | semidirect |
| 192. C32 | #3392 | semidirect |
| 196. Q8 | #3744 | semidirect |
| 209. C8 | #3832 | semidirect |
| 225. C3 | #79911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596048 | 2 |
| #10596041 | 2 |
| C32×C8×Q8 | 2 |
| #10592547 | 2 |
| #10592540 | 2 |
| #10592392 | 2 |
| C4×#3744 | 2 |
| #79911 | 3 |