Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
552 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 180 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 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C32 |
| prime radical | C2×C32×D4 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C32×C42 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×#501 | C2 | semidirect |
| 3. C32×#491 | C2 | semidirect |
| 5. C32×#330 | C2 | semidirect |
| 6. C32×#330 | C2 | semidirect |
| 8. C3×#1664 | C3 | direct (N × H) |
| 29. C3×#501 | C2×C3 | semidirect |
| 30. C3×#491 | C2×C3 | semidirect |
| 32. C3×#330 | C2×C3 | semidirect |
| 33. C3×#330 | C2×C3 | semidirect |
| 62. #1664 | C32 | direct (N × H) |
| 101. #501 | C2×C32 | semidirect |
| 102. #491 | C2×C32 | semidirect |
| 104. #330 | C2×C32 | semidirect |
| 105. #330 | C2×C32 | semidirect |
| 228. C32 | #1664 | direct (N × H) |
| 264. C3 | C3×#1664 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#563 | 2 |
| C32×#501 | 2 |
| C32×#491 | 2 |
| C32×#489 | 2 |
| C32×#330 | 2 |
| C32×#329 | 2 |
| C3×#1664 | 3 |