Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
853 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 853 conjugacy classes of subgroups — too many to draw. Only its 276 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D32 |
| commutator, socle | C2×C32 | C23×C8 |
| Fitting | C32×#131 | C22 |
| prime radical | #41×C3⋊D3 | C4 |
| cosocle | C32×C8 | C24 |
| hypercenter | #131 | D32 |
| hypocenter | C32 | #3407 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C8 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#5140 | C2 | semidirect |
| 3. C2×#63544 | C2 | semidirect |
| 4. #10590625 | C2 | semidirect |
| 5. #10590624 | C2 | semidirect |
| 14. C3×#812 | C22 | semidirect |
| 15. C2×C3×C3⋊C16 | C22 | semidirect |
| 18. #63544 | C22 | semidirect |
| 19. #63542 | C22 | semidirect |
| 23. #5140 | D3 | semidirect |
| 63. #812 | C2×D3 | semidirect |
| 64. C2×C3⋊C16 | C2×D3 | semidirect |
| 218. C32 | #3407 | semidirect |
| 252. C3 | #82012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#131 | 2 |
| C3×#5140 | 2 |
| C2×#63544 | 2 |
| #10590625 | 2 |
| #10590624 | 2 |
| #82012 | 3 |