Finite Group DatabasebetaFinite Group Databasebeta← ΓL(1,𝔽8)×#13095276 #44567151
Order 32193.
56 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C73 | C32 |
| LCS | G ▷ C72×C73 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #24924362 | C3 | semidirect |
| 2. C7×ΓL(1,𝔽8)×C73 | C3 | semidirect |
| 3. C7×#13095276 | C3 | semidirect |
| 4. C73⋊#3862 | C3 | semidirect |
| 7. C72×C73 | C32 | semidirect |
| 13. #13095276 | ΓL(1,𝔽8) | direct (N × H) |
| 16. ΓL(1,𝔽8)×C73 | ΓL(1,𝔽8) | semidirect |
| 19. C7×C73 | C3×ΓL(1,𝔽8) | semidirect |
| 20. C7×C73 | C3×ΓL(1,𝔽8) | semidirect |
| 29. C7×ΓL(1,𝔽8) | C73⋊C3 | semidirect |
| 30. C73 | ΓL(1,𝔽8)2 | semidirect |
| 33. C72 | C3×C73⋊C3 | semidirect |
| 42. ΓL(1,𝔽8) | #13095276 | direct (N × H) |
| 45. C7 | ΓL(1,𝔽8)×C73⋊C3 | semidirect |
| 46. C7 | C3×#13095276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924362 | 3 |
| C7×ΓL(1,𝔽8)×C73 | 3 |
| C7×#13095276 | 3 |
| C73⋊#3862 | 3 |
| C3×#13095276 | 7 |
| ΓL(1,𝔽8)×C73⋊C3 | 7 |
| ΓL(1,𝔽8)2 | 73 |