Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
456 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C22×D67 |
| commutator | C2×C67 | C23×C8 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | C8×Q8×C67 | C2 |
| socle | C22×C67 | C23×C4 |
| hypercenter | C8×Q8 | D67 |
| hypocenter | C67 | C8×#41 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C8 ◁ C8×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×C67⋊C8 | C2 | semidirect |
| 3. C8×D268 | C2 | semidirect |
| 4. #16863461 | C2 | semidirect |
| 5. #16863448 | C2 | semidirect |
| 6. C4×C8×D67 | C2 | semidirect |
| 7. C8×Q8×C67 | C2 | semidirect |
| 24. #11761629 | C8 | direct (N × H) |
| 44. Q8×C67 | C2×C8 | semidirect |
| 51. D268 | C2×C8 | semidirect |
| 55. C4×D67 | C2×C8 | semidirect |
| 57. C8×C67 | #41 | semidirect |
| 59. C67⋊C8 | #41 | semidirect |
| 76. C67 | C8×#41 | semidirect |
| 79. C8×Q8 | D67 | semidirect |
| 120. Q8 | C8×D67 | semidirect |
| 135. C8 | #11761629 | direct (N × H) |