Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
676 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator, socle | C23×C67 | C24 |
| Fitting | C2×C4×Q8×C67 | C2 |
| hypercenter | C2×C4×Q8 | D67 |
| hypocenter | C67 | #2548 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14524032 | C2 | semidirect |
| 3. #16863313 | C2 | semidirect |
| 4. #16863298 | C2 | semidirect |
| 5. #16863297 | C2 | semidirect |
| 6. C4×C4⋊Dic67 | C2 | semidirect |
| 7. C2×C4×Q8×C67 | C2 | semidirect |
| 39. C2×Q8×C67 | D4 | semidirect |
| 88. C4×C67 | #124 | semidirect |
| 97. C67 | #2548 | semidirect |
| 100. C2×C4×Q8 | D67 | semidirect |
| 124. C2×Q8 | D268 | semidirect |
| 186. C4 | #14524032 | semidirect |