Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
224 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 122 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×C4 | C22×#6923 |
| commutator | C2×C61 | C2×C4×C8 |
| Fitting | C2×M16×C61 | C4 |
| socle | C22×C61 | C2×C42 |
| hypercenter | C2×M16 | #6923 |
| hypocenter | C61 | C8×M16 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16840603 | C2 | semidirect |
| 4. C8×#92420 | C2 | semidirect |
| 25. M16×C61 | C8 | semidirect |
| 31. #11758194 | C8 | semidirect |
| 46. #92420 | M16 | direct (N × H) |
| 47. C8×C61 | C2×C8 | semidirect |
| 48. #92418 | C2×C8 | semidirect |
| 70. C61 | C8×M16 | semidirect |
| 87. M16 | #92420 | direct (N × H) |
| 113. C8 | C2×#92420 | semidirect |