Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14524015 |
| commutator | C42×C67 | C23 |
| Frattini | C42 | C22×D67 |
| Fitting | #460×C67 | C2 |
| socle | C22×C67 | #121 |
| hypercenter | #460 | D67 |
| hypocenter | C67 | #1668 |
| LCS | G ▷ C42×C67 ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #460 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863596 | C2 | semidirect |
| 3. Q8×C67⋊C8 | C2 | semidirect |
| 4. #16863148 | C2 | semidirect |
| 5. #16863140 | C2 | semidirect |
| 6. #16863139 | C2 | semidirect |
| 7. #460×C67 | C2 | semidirect |
| 46. Q8×C67 | D8 | semidirect |
| 66. C67⋊C8 | SD16 | semidirect |
| 87. C67 | #1668 | semidirect |
| 90. #460 | D67 | semidirect |
| 133. Q8 | #11761613 | semidirect |