Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×D268 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #436×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #436 | D67 |
| hypocenter | C67 | #3276 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ #436 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524076 | C2 | semidirect |
| 2. D4×Dic134 | C2 | semidirect |
| 4. #16863776 | C2 | semidirect |
| 5. #16863654 | C2 | semidirect |
| 6. #16863607 | C2 | semidirect |
| 7. #16863602 | C2 | semidirect |
| 8. #16863560 | C2 | semidirect |
| 9. #16863554 | C2 | semidirect |
| 10. C4×#11761617 | C2 | semidirect |
| 11. #436×C67 | C2 | semidirect |
| 59. #11761617 | D4 | semidirect |
| 121. C4×C67 | #137 | semidirect |
| 135. C67 | #3276 | semidirect |
| 146. #436 | D67 | semidirect |
| 261. C4 | #14524076 | semidirect |