Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C22⋊D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | Q82×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | Q82 | D67 |
| hypocenter | C67 | #3362 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 ◁ Q82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863744 | C2 | semidirect |
| 3. #16863683 | C2 | semidirect |
| 4. #16863596 | C2 | semidirect |
| 5. Q8×C67⋊C8 | C2 | semidirect |
| 6. C4×#11761615 | C2 | semidirect |
| 7. Q82×C67 | C2 | semidirect |
| 46. Q8×C67 | SD16 | semidirect |
| 47. Q8×C67 | #41 | semidirect |
| 77. C67 | #3362 | semidirect |
| 78. Q82 | D67 | semidirect |
| 123. Q8 | #11761615 | semidirect |
| 124. Q8 | #11761629 | semidirect |