Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
390 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C32 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C32 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C32×C42 ◁ C32×C4×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C3×#2225 | C3 | direct (N × H) |
| 24. C32×Q16 | Q8 | semidirect |
| 34. #2225 | C32 | direct (N × H) |
| 64. C3×Q16 | C3×Q8 | semidirect |
| 109. Q16 | C32×Q8 | semidirect |
| 127. C32 | #2225 | direct (N × H) |
| 151. C3 | C3×#2225 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#500 | 2 |
| C32×C4×Q16 | 2 |
| C32×#367 | 2 |
| C32×C4⋊C16 | 2 |
| C32×#358 | 2 |
| C3×#2225 | 3 |