Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1944 conjugacy classes of subgroups; only the 1308 normal subgroups are shown.
This group has 1944 conjugacy classes of subgroups — too many to draw. Only its 1308 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C9 | C24 |
| commutator | C22 | C25×C9 |
| Frattini, cosocle | C22×C3 | C25×C3 |
| socle | C23×C3 | C24×C3 |
| prime radical | C25×C3 | C22×C3 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C9 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#543 | C2 | direct (N × H) |
| 2. C2×C9×C22⋊Q8 | C2 | semidirect |
| 6. C22×Q8×C9 | C22 | semidirect |
| 8. C9×C22⋊Q8 | C22 | semidirect |
| 9. C2×C9×C4⋊C4 | C22 | semidirect |
| 16. C24×C9 | Q8 | semidirect |
| 20. C2×Q8×C9 | C23 | semidirect |
| 24. C9×C4⋊C4 | C23 | semidirect |
| 26. C2×#543 | C9 | direct (N × H) |
| 38. C23×C9 | C2×Q8 | semidirect |
| 45. #543 | C2×C9 | direct (N × H) |
| 46. C2×C22⋊Q8 | C2×C9 | semidirect |
| 68. C22×Q8 | C22×C9 | semidirect |
| 70. C22⋊Q8 | C22×C9 | semidirect |
| 71. C2×C4⋊C4 | C22×C9 | semidirect |
| 86. C2×C9 | #543 | direct (N × H) |
| 90. C24 | Q8×C9 | semidirect |
| 94. C2×Q8 | C23×C9 | semidirect |
| 98. C4⋊C4 | C23×C9 | semidirect |
| 108. C9 | C2×#543 | direct (N × H) |
| 113. C23 | C2×Q8×C9 | semidirect |
| 134. C2 | C9×#543 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#543 | 2 |
| C2×C9×C22⋊Q8 | 2 |
| C22×C9×C22⋊C4 | 2 |
| C2×C3×#543 | 3 |