Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1624 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 1624 conjugacy classes of subgroups — too many to draw. Only its 725 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×D67 |
| commutator | C22×C67 | C25 |
| Frattini | C22 | C24×D67 |
| Fitting | C22×C4⋊C4×C67 | C2 |
| socle | C24×C67 | C23 |
| hypercenter | C22×C4⋊C4 | D67 |
| hypocenter | C67 | C22×C4⋊Q8 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14524042 | C2 | direct (N × H) |
| 12. #14524042 | C22 | direct (N × H) |
| 23. C22×Dic67 | Q8 | semidirect |
| 32. C22×C4×C67 | Q8 | semidirect |
| 41. C2×C4×C67 | C2×Q8 | semidirect |
| 46. C2×Dic67 | C2×Q8 | semidirect |
| 51. C22×C67 | C4⋊Q8 | semidirect |
| 57. C4×C67 | C22×Q8 | semidirect |
| 60. Dic67 | C22×Q8 | semidirect |
| 61. C2×C67 | C2×C4⋊Q8 | semidirect |
| 66. C67 | C22×C4⋊Q8 | semidirect |
| 95. C22×C4 | Dic134 | semidirect |
| 114. C2×C4 | C2×Dic134 | semidirect |
| 117. C22 | #14524042 | direct (N × H) |
| 126. C4 | C22×Dic134 | semidirect |
| 127. C2 | C2×#14524042 | direct (N × H) |