Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
858 conjugacy classes of subgroups.
The subgroup lattice has 396 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C113 | #121 |
| commutator | C2×C4 | C23×C4×C113 |
| Frattini, cosocle | C22×C4 | C24×C113 |
| socle | C22×C113 | #389 |
| prime radical | C24×C113 | C2×Q8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C113 ◁ C23×C4×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C113×#1953 | C2 | direct (N × H) |
| 18. C2×#108×C113 | C4 | semidirect |
| 19. C2×#108×C113 | C4 | semidirect |
| 67. #108×C113 | C2×C4 | semidirect |
| 189. C2×#1953 | C113 | direct (N × H) |
| 196. C2×C113 | #1953 | direct (N × H) |
| 202. #1953 | C2×C113 | direct (N × H) |
| 204. C113 | C2×#1953 | direct (N × H) |
| 216. C2×#108 | C4×C113 | semidirect |
| 217. C2×#108 | C4×C113 | semidirect |
| 265. #108 | C2×C4×C113 | semidirect |
| 393. C2 | C113×#1953 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#430×C113 | 2 |
| C22×#108×C113 | 2 |
| C2×#405×C113 | 2 |
| C113×#1953 | 2 |
| C2×#344×C113 | 2 |
| C2×#1953 | 113 |