Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
924 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 133 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. #10592769 | C2 | semidirect |
| 3. #10592545 | C2 | semidirect |
| 4. #10592540 | C2 | semidirect |
| 5. C32×#331 | C2 | semidirect |
| 6. #10589349 | C2 | semidirect |
| 7. #10589349 | C2 | semidirect |
| 18. #64078 | C22 | semidirect |
| 19. C32×C4⋊C8 | C22 | semidirect |
| 20. C32×C4⋊C8 | C22 | semidirect |
| 25. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 30. C3×#331 | D3 | semidirect |
| 71. C3×C4⋊C8 | C2×D3 | semidirect |
| 72. C3×C4⋊C8 | C2×D3 | semidirect |
| 100. C4⋊(C3⋊D3) | SD16 | semidirect |
| 114. #331 | C3⋊D3 | semidirect |
| 174. C4⋊C8 | C2×C3⋊D3 | semidirect |
| 175. C4⋊C8 | C2×C3⋊D3 | semidirect |
| 264. C32 | #1639 | semidirect |
| 322. C3 | #68392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596188 | 2 |
| #10592769 | 2 |
| #10592545 | 2 |
| #10592540 | 2 |
| C32×#331 | 2 |
| #10589349 | 2 |
| #68392 | 3 |