Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1800 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C43 | C24 |
| commutator | C22 | C24×C4×C43 |
| Frattini, cosocle | C23 | C25×C43 |
| socle, prime radical | C23×C43 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C43×#564 | C4 | direct (N × H) |
| 33. C4×#564 | C43 | direct (N × H) |
| 39. C4×C43 | #564 | direct (N × H) |
| 46. #564 | C4×C43 | direct (N × H) |
| 53. C43 | C4×#564 | direct (N × H) |
| 81. C4 | C43×#564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C43×#564 | 2 |
| C43×#2382 | 2 |
| C4×#125×C43 | 2 |
| C4×#564 | 43 |