Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
210 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14519746 |
| commutator | C42×C61 | C23 |
| Frattini | C42 | C22×D61 |
| Fitting | C61×#557 | C2 |
| socle | C22×C61 | #120 |
| hypercenter | #557 | D61 |
| hypocenter | C61 | #1626 |
| LCS | G ▷ C42×C61 ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #557 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #16839508 | C2 | semidirect |
| 5. Q8⋊#92418 | C2 | semidirect |
| 6. Q8⋊#92418 | C2 | semidirect |
| 7. C61×#557 | C2 | semidirect |
| 55. Q8×C61 | SD16 | semidirect |
| 91. #557 | D61 | semidirect |
| 98. C61 | #1626 | semidirect |
| 146. Q8 | #11758201 | semidirect |