Finite Group DatabasebetaFinite Group DatabasebetaOrder 10804.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C37×C73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C37×C73 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | Dic73 | — | 37 | 1 | no | maximal, Hall |
| 4 | Dic37 | — | 73 | 1 | no | maximal, Hall |
| 5 | C2×C73 | D37 | 1 | 1 | yes | characteristic |
| 6 | C2×C37 | D73 | 1 | 1 | yes | characteristic |
| 7 | C73 | Dic37 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 8 | C37 | Dic73 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C4 | — | 2701 | 1 | no | Sylow |
| 10 | C2 | D2701 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2701 |
| commutator, hypocenter | C37×C73 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C37×C73 | C2 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C37×C73 | C4 | semidirect |
| 7. C73 | Dic37 | semidirect |
| 8. C37 | Dic73 | semidirect |