Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
626 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 238 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×#157 |
| commutator, socle | C2×C32 | C23×C8 |
| Fitting, prime radical | C2×C32×#41 | C4 |
| cosocle | C3⋊(C3⋊C8) | C24 |
| hypercenter | C2×#41 | #157 |
| hypocenter | C32 | #3407 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10593838 | C2 | semidirect |
| 3. C2×#63773 | C2 | semidirect |
| 10. #63773 | C22 | semidirect |
| 11. C2×#3708 | C22 | semidirect |
| 97. C32 | #3407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64157 | 2 |
| #10593838 | 2 |
| C2×#63773 | 2 |
| #3407 | 9 |