Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
552 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 552 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 | C22×C32 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C32 |
| prime radical | C32×#493 | C2 |
| 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×#460 | C2 | semidirect |
| 3. C32×#446 | C2 | semidirect |
| 4. C32×#334 | C2 | semidirect |
| 5. C32×#331 | C2 | semidirect |
| 6. C3×#1688 | C3 | direct (N × H) |
| 19. C3×#460 | C2×C3 | semidirect |
| 20. C3×#446 | C2×C3 | semidirect |
| 21. C3×#334 | C2×C3 | semidirect |
| 22. C3×#331 | C2×C3 | semidirect |
| 38. #1688 | C32 | direct (N × H) |
| 65. C32×C8 | SD16 | semidirect |
| 67. #460 | C2×C32 | semidirect |
| 68. #446 | C2×C32 | semidirect |
| 69. #334 | C2×C32 | semidirect |
| 70. #331 | C2×C32 | semidirect |
| 122. C3×C8 | C3×SD16 | semidirect |
| 152. C32 | #1688 | direct (N × H) |
| 168. C8 | C32×SD16 | semidirect |
| 183. C3 | C3×#1688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| C32×#460 | 2 |
| C32×#446 | 2 |
| C32×#334 | 2 |
| C32×#331 | 2 |
| C3×#1688 | 3 |