Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1720 conjugacy classes of subgroups; only the 810 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 810 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6923 |
| commutator | C2×C61 | C24×C4 |
| Frattini | C2 | C24×#6923 |
| Fitting | C23×C4×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C23×C4 | #6923 |
| hypocenter | C61 | C23×M16 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11758213 | C2 | semidirect |
| 2. C2×D61⋊M16 | C2 | direct (N × H) |
| 3. C22×#11758217 | C2 | semidirect |
| 4. C22×D61⋊C8 | C2 | semidirect |
| 6. C2×#11758213 | C22 | semidirect |
| 7. D61⋊M16 | C22 | direct (N × H) |
| 8. C2×#11758217 | C22 | semidirect |
| 9. C2×D61⋊C8 | C22 | semidirect |
| 10. C22×#92420 | C22 | semidirect |
| 40. #11758217 | C23 | semidirect |
| 41. C2×#92420 | C23 | semidirect |
| 42. #11758213 | C23 | semidirect |
| 43. D61⋊C8 | C23 | semidirect |
| 49. C22×D61 | M16 | semidirect |
| 67. #92420 | C24 | semidirect |
| 69. C22×C61 | C2×M16 | semidirect |
| 74. C2×D61 | C2×M16 | semidirect |
| 84. C2×C61 | C22×M16 | semidirect |
| 87. D61 | C22×M16 | semidirect |
| 93. C61 | C23×M16 | semidirect |
| 162. C22 | D61⋊M16 | direct (N × H) |
| 173. C2 | C2×D61⋊M16 | direct (N × H) |