Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
516 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C32 | #99 |
| commutator | C2×C4 | C32×C42 |
| Frattini, cosocle | C22×Q8 | C22×C32 |
| prime radical | C23×C32 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C23×C32 ◁ C22×C32×Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#1394 | C3 | direct (N × H) |
| 9. C32×#101 | C4 | semidirect |
| 27. #1394 | C32 | direct (N × H) |
| 33. C3×#101 | C3×C4 | semidirect |
| 85. #101 | C32×C4 | semidirect |
| 135. C32 | #1394 | direct (N × H) |
| 170. C3 | C3×#1394 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#101 | 2 |
| C32×#391 | 2 |
| C3×#1394 | 3 |