Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2796 conjugacy classes of subgroups; only the 696 normal subgroups are shown.
This group has 2796 conjugacy classes of subgroups — too many to draw. Only its 696 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C32 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C32 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C32×#41 | C2 | semidirect |
| 2. C2×C32×#121 | C2 | semidirect |
| 3. C32×#393 | C2 | semidirect |
| 4. C32×#392 | C2 | semidirect |
| 5. C32×#380 | C2 | semidirect |
| 6. C3×#2615 | C3 | direct (N × H) |
| 18. C22×C3×#41 | C2×C3 | semidirect |
| 19. C2×C3×#121 | C2×C3 | semidirect |
| 20. C3×#393 | C2×C3 | semidirect |
| 21. C3×#392 | C2×C3 | semidirect |
| 22. C3×#380 | C2×C3 | semidirect |
| 33. C22×C32×C4 | D4 | semidirect |
| 40. #2615 | C32 | direct (N × H) |
| 71. C22×#41 | C2×C32 | semidirect |
| 72. C2×#121 | C2×C32 | semidirect |
| 73. #393 | C2×C32 | semidirect |
| 74. #392 | C2×C32 | semidirect |
| 75. #380 | C2×C32 | semidirect |
| 86. C22×C3×C4 | C3×D4 | semidirect |
| 152. C22×C4 | C32×D4 | semidirect |
| 173. C32 | #2615 | direct (N × H) |
| 212. C3 | C3×#2615 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×#41 | 2 |
| C2×C32×#121 | 2 |
| C32×#393 | 2 |
| C32×#392 | 2 |
| C32×#380 | 2 |
| C3×#2615 | 3 |