Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
528 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 137 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. #10592711 | C2 | semidirect |
| 3. #10592537 | C2 | semidirect |
| 4. C32×D4⋊C8 | C2 | semidirect |
| 5. #10589346 | C2 | semidirect |
| 6. #10589325 | C2 | semidirect |
| 7. #10589320 | C2 | semidirect |
| 27. C3×D4⋊C8 | D3 | semidirect |
| 87. C3⋊(C3⋊C8) | M16 | semidirect |
| 93. D4⋊C8 | C3⋊D3 | semidirect |
| 203. C32 | #1594 | semidirect |
| 245. C3 | #68163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3753 | 2 |
| #10592711 | 2 |
| #10592537 | 2 |
| C32×D4⋊C8 | 2 |
| #10589346 | 2 |
| #10589325 | 2 |
| #10589320 | 2 |
| #68163 | 3 |