Finite Group DatabasebetaFinite Group DatabasebetaOrder 10688.
106 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C167 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C167 |
| prime radical | #121×C167 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C167 ◁ C22×C4×C167 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #117×C167 | C2 | semidirect |
| 3. #107×C167 | C2 | semidirect |
| 4. #106×C167 | C2 | semidirect |
| 5. #102×C167 | C2 | semidirect |
| 6. #102×C167 | C2 | semidirect |
| 7. C22⋊C8×C167 | C2 | semidirect |
| 51. C167 | #482 | direct (N × H) |
| 52. #482 | C167 | direct (N × H) |
| 54. #117 | C2×C167 | semidirect |
| 55. #107 | C2×C167 | semidirect |
| 56. #106 | C2×C167 | semidirect |
| 57. #102 | C2×C167 | semidirect |
| 58. #102 | C2×C167 | semidirect |
| 59. C22⋊C8 | C2×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #121×C167 | 2 |
| #117×C167 | 2 |
| #107×C167 | 2 |
| #106×C167 | 2 |
| #102×C167 | 2 |
| C22⋊C8×C167 | 2 |
| #482 | 167 |