Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
1800 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C107 | C24 |
| commutator | C22 | C24×C4×C107 |
| Frattini, cosocle | C23 | C25×C107 |
| socle, prime radical | C23×C107 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #564×C107 | C4 | direct (N × H) |
| 38. C4×C107 | #564 | direct (N × H) |
| 39. C4×#564 | C107 | direct (N × H) |
| 46. C107 | C4×#564 | direct (N × H) |
| 47. #564 | C4×C107 | direct (N × H) |
| 81. C4 | #564×C107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#564×C107 | 2 |
| C107×#2382 | 2 |
| C4×#125×C107 | 2 |
| C4×#564 | 107 |