Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
2942 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C107 | C23 |
| commutator | C23 | C23×C4×C107 |
| Frattini, cosocle | C24 | C24×C107 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C107×#1445 | C2 | direct (N × H) |
| 12. C22×C4⋊C4×C107 | C4 | semidirect |
| 47. C2×C4⋊C4×C107 | C2×C4 | semidirect |
| 174. C2×#1445 | C107 | direct (N × H) |
| 175. C2×C107 | #1445 | direct (N × H) |
| 188. #1445 | C2×C107 | direct (N × H) |
| 189. C107 | C2×#1445 | direct (N × H) |
| 196. C22×C4⋊C4 | C4×C107 | semidirect |
| 231. C2×C4⋊C4 | C2×C4×C107 | semidirect |
| 358. C2 | C107×#1445 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊C4×C107 | 2 |
| C22×#95×C107 | 2 |
| C107×#1445 | 2 |
| C2×#1445 | 107 |