Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1252 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 261 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D61 |
| commutator | C23×C61 | C24 |
| Frattini | C23 | C23×D61 |
| Fitting | C22×C4⋊C4×C61 | C2 |
| socle | C24×C61 | C23 |
| hypercenter | C22×C4⋊C4 | D61 |
| hypocenter | C61 | C2×#394 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#11758198 | C2 | semidirect |
| 3. C22×#11758198 | C2 | semidirect |
| 4. #16839679 | C2 | direct (N × H) |
| 5. C2×#14519684 | C2 | semidirect |
| 6. C22×C4⋊C4×C61 | C2 | semidirect |
| 14. C2×#11758198 | C22 | semidirect |
| 15. C2×#11758198 | C22 | semidirect |
| 16. #14519684 | C22 | semidirect |
| 21. C2×C4⋊C4×C61 | C22 | semidirect |
| 37. C22×C4×C61 | D4 | semidirect |
| 80. C2×C4×C61 | C2×D4 | semidirect |
| 109. C2×C61 | #394 | semidirect |
| 117. C22×C4⋊C4 | D61 | semidirect |
| 122. C61 | C2×#394 | semidirect |
| 132. C2×C4⋊C4 | C2×D61 | semidirect |
| 159. C22×C4 | D244 | semidirect |
| 200. C2×C4 | C2×D244 | semidirect |
| 225. C2 | #16839679 | direct (N × H) |