Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D61 |
| commutator | C22×C4×C61 | C23 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C61×#340 | C2 |
| socle | C23×C61 | C2×D4 |
| hypercenter | #340 | D61 |
| hypocenter | C61 | #1999 |
| LCS | G ▷ C22×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D488 | C2 | semidirect |
| 2. C2×#14519752 | C2 | semidirect |
| 3. C2×#14519697 | C2 | semidirect |
| 4. C2×#14519689 | C2 | semidirect |
| 5. C61×#340 | C2 | semidirect |
| 32. C2×D244 | D4 | semidirect |
| 38. C2×C8×C61 | D4 | semidirect |
| 40. C4⋊C4×C61 | D4 | semidirect |
| 57. C22×D61 | D8 | semidirect |
| 111. #340 | D61 | semidirect |
| 112. C61 | #1999 | semidirect |
| 148. C2×C8 | D244 | semidirect |
| 150. C4⋊C4 | D244 | semidirect |