Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
1222 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C113 | C23 |
| commutator | C23 | C23×C4×C113 |
| Frattini, cosocle | C24 | C24×C113 |
| socle, prime radical | C24×C113 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #401×C113 | C4 | direct (N × H) |
| 38. C4×C113 | #401 | direct (N × H) |
| 39. C4×#401 | C113 | direct (N × H) |
| 46. C113 | C4×#401 | direct (N × H) |
| 48. #401 | C4×C113 | direct (N × H) |
| 81. C4 | #401×C113 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#401×C113 | 2 |
| C113×#1443 | 2 |
| C4×#95×C113 | 2 |
| C4×#401 | 113 |