Finite Group DatabasebetaFinite Group DatabasebetaOrder 5887.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C292 | C7 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C29⋊C7 | — | 29 | 2 | no | maximal |
| 3 | C29 | — | 7 | 4 | no | — |
| 4 | C29 | C29⋊C7 | 1 | 2 | yes | complemented |
| 5 | C7 | — | 841 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C292 | C7 |
| LCS | G ▷ C292 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C292 | C7 | semidirect |
| 4. C29 | C29⋊C7 | semidirect |