Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
164 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D61 |
| commutator, socle | C22×C61 | C22×C8 |
| Fitting | C61×C4⋊C16 | C2 |
| hypercenter | C4⋊C16 | D61 |
| hypocenter | C61 | #2168 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C8 ◁ C4⋊C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519716 | C2 | semidirect |
| 2. C2×C16×D61 | C2 | semidirect |
| 4. #16839541 | C2 | semidirect |
| 5. #16839541 | C2 | semidirect |
| 6. #16839538 | C2 | semidirect |
| 7. C61×C4⋊C16 | C2 | semidirect |
| 39. #11758185 | D4 | semidirect |
| 63. C2×D61 | M32 | semidirect |
| 79. C4⋊C16 | D61 | semidirect |
| 83. C61 | #2168 | semidirect |