Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
290 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D167 |
| commutator, socle, cosocle | C22×C167 | C24 |
| Fitting | C4×Q8×C167 | C2 |
| hypercenter | C4×Q8 | D167 |
| hypocenter | C167 | #548 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14581951 | C2 | semidirect |
| 2. C2×Q8×D167 | C2 | semidirect |
| 3. #19128820 | C2 | semidirect |
| 4. #19128812 | C2 | semidirect |
| 5. #19128807 | C2 | semidirect |
| 6. C4×D668 | C2 | semidirect |
| 7. C4×Q8×C167 | C2 | semidirect |
| 31. Q8×C167 | D4 | semidirect |
| 41. C2×D167 | #41 | semidirect |
| 52. C167 | #548 | semidirect |
| 59. C4×Q8 | D167 | semidirect |
| 78. Q8 | D668 | semidirect |