Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
272 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D67 |
| commutator | C2×C67 | C22×C16 |
| Fitting | C22⋊C16×C67 | C2 |
| socle | C22×C67 | C22×C8 |
| hypercenter | C22⋊C16 | D67 |
| hypocenter | C67 | C2×C22⋊C16 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2×C8 ◁ C22⋊C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C16×D67 | C2 | semidirect |
| 3. C22⋊(C67⋊C16) | C2 | semidirect |
| 4. (C2×D67)⋊C16 | C2 | semidirect |
| 5. C22⋊C16×C67 | C2 | semidirect |
| 13. C2×C67⋊C16 | C22 | semidirect |
| 16. C2×C16×C67 | C22 | semidirect |
| 41. C22×D67 | C16 | semidirect |
| 63. C22×C67 | C2×C16 | semidirect |
| 70. C2×D67 | C2×C16 | semidirect |
| 82. D67 | C22⋊C16 | direct (N × H) |
| 84. C67 | C2×C22⋊C16 | semidirect |
| 89. C22⋊C16 | D67 | direct (N × H) |
| 100. C2×C16 | C2×D67 | semidirect |
| 154. C22 | C16×D67 | semidirect |