Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
840 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 840 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 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C32 |
| prime radical | C32×#534 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C22×C32×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×#480 | C2 | semidirect |
| 3. C32×#397 | C2 | semidirect |
| 4. C32×#327 | C2 | semidirect |
| 5. C32×#323 | C2 | semidirect |
| 6. C3×#1607 | C3 | direct (N × H) |
| 12. C2×C32×C4⋊C4 | C22 | semidirect |
| 17. C32×C22⋊C8 | C22 | semidirect |
| 19. C32×#95 | C22 | semidirect |
| 21. C3×#480 | C2×C3 | semidirect |
| 22. C3×#397 | C2×C3 | semidirect |
| 23. C3×#327 | C2×C3 | semidirect |
| 24. C3×#323 | C2×C3 | semidirect |
| 46. #1607 | C32 | direct (N × H) |
| 52. C2×C3×C4⋊C4 | C22×C3 | semidirect |
| 57. C3×C22⋊C8 | C22×C3 | semidirect |
| 59. C3×#95 | C22×C3 | semidirect |
| 89. #480 | C2×C32 | semidirect |
| 90. #397 | C2×C32 | semidirect |
| 91. #327 | C2×C32 | semidirect |
| 92. #323 | C2×C32 | semidirect |
| 138. C2×C4⋊C4 | C22×C32 | semidirect |
| 143. C22⋊C8 | C22×C32 | semidirect |
| 145. #95 | C22×C32 | semidirect |
| 221. C32 | #1607 | direct (N × H) |
| 276. C3 | C3×#1607 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#534 | 2 |
| C32×#480 | 2 |
| C32×#397 | 2 |
| C32×#327 | 2 |
| C32×#323 | 2 |
| C3×#1607 | 3 |