Finite Group DatabasebetaFinite Group DatabasebetaOrder 7748.
12 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | D1937 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C13×C149 | C4 | 1 | 1 | yes | characteristic, complemented, Hall |
| 3 | #10597010 | — | 13 | 1 | no | maximal, Hall |
| 4 | D149 | — | 13 | 1 | no | — |
| 5 | C149 | #261 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 6 | #261 | — | 149 | 1 | no | maximal, Hall |
| 7 | D13 | — | 149 | 1 | no | — |
| 8 | C13 | #10597010 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C4 | — | 1937 | 1 | no | Sylow |
| 10 | C2 | — | 1937 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C149 | C4 |
| LCS | G ▷ C13×C149 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C13×C149 | C4 | semidirect |
| 5. C149 | #261 | semidirect |
| 8. C13 | #10597010 | semidirect |