Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
512 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 280 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C167 | C24 |
| commutator | C22 | C23×C4×C167 |
| Frattini, cosocle | C23 | C24×C167 |
| prime radical | C24×C167 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C167 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #387×C167 | C2 | semidirect |
| 9. C2×C4⋊C4×C167 | C4 | semidirect |
| 66. C167 | #2313 | direct (N × H) |
| 67. #2313 | C167 | direct (N × H) |
| 69. #387 | C2×C167 | semidirect |
| 76. C2×C4⋊C4 | C4×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊C4×C167 | 2 |
| #387×C167 | 2 |
| #381×C167 | 2 |
| #380×C167 | 2 |
| C4×C22⋊C4×C167 | 2 |
| #2313 | 167 |