Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14519752 |
| commutator | C42×C61 | C23 |
| Frattini | C42 | C22×D61 |
| Fitting | C61×#335 | C2 |
| socle | C22×C61 | #121 |
| hypercenter | #335 | D61 |
| hypocenter | C61 | #1697 |
| LCS | G ▷ C42×C61 ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #335 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16840109 | C2 | semidirect |
| 2. #16840053 | C2 | semidirect |
| 4. #16839841 | C2 | semidirect |
| 5. #16839510 | C2 | semidirect |
| 6. #16839505 | C2 | semidirect |
| 7. C61×#335 | C2 | semidirect |
| 87. #335 | D61 | semidirect |
| 90. C61 | #1697 | semidirect |