Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 525 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 | C4×C61 | C25 |
| Frattini | C4 | C24×D61 |
| Fitting | C22×Q16×C61 | C2 |
| socle | C23×C61 | C2×D4 |
| hypercenter | C22×Q16 | D61 |
| hypocenter | C61 | C22×#135 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×Q16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11758226 | C2 | semidirect |
| 2. C2×#14519800 | C2 | direct (N × H) |
| 3. C22×#11758201 | C2 | semidirect |
| 4. C22×D488 | C2 | semidirect |
| 5. C22×C8×D61 | C2 | semidirect |
| 6. C22×Q16×C61 | C2 | semidirect |
| 8. C2×#11758226 | C22 | semidirect |
| 13. #14519800 | C22 | direct (N × H) |
| 14. C2×#11758201 | C22 | semidirect |
| 15. C2×D488 | C22 | semidirect |
| 17. C2×C8×D61 | C22 | semidirect |
| 19. C2×Q16×C61 | C22 | semidirect |
| 29. #11758226 | C23 | semidirect |
| 36. Q16×C61 | C23 | semidirect |
| 38. #11758201 | C23 | semidirect |
| 40. D488 | C23 | semidirect |
| 41. C8×D61 | C23 | semidirect |
| 61. C22×C61 | #135 | semidirect |
| 72. C2×C61 | C2×#135 | semidirect |
| 78. C22×Q16 | D61 | semidirect |
| 82. C61 | C22×#135 | semidirect |
| 91. C2×Q16 | C2×D61 | semidirect |
| 112. Q16 | C22×D61 | semidirect |
| 141. C22 | #14519800 | direct (N × H) |
| 149. C2 | C2×#14519800 | direct (N × H) |