Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
804 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator, socle | C23×C61 | C24 |
| Fitting | C61×#392 | C2 |
| hypercenter | #392 | D61 |
| hypocenter | C61 | #2656 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519750 | C2 | semidirect |
| 2. C2×#14519748 | C2 | semidirect |
| 3. #16839699 | C2 | semidirect |
| 4. #16839698 | C2 | semidirect |
| 5. #16839670 | C2 | semidirect |
| 6. #95×D61 | C2 | semidirect |
| 7. C61×#392 | C2 | semidirect |
| 37. C2×C4×D61 | D4 | semidirect |
| 97. #392 | D61 | semidirect |
| 99. C61 | #2656 | semidirect |