Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
124 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C167 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C23×C167 |
| prime radical | C23×C167 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C167 ◁ C2×C4×C167 ◁ C2×M16×C167 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #365×C167 | C2 | semidirect |
| 4. #362×C167 | C2 | semidirect |
| 51. C167 | #2239 | direct (N × H) |
| 52. #2239 | C167 | direct (N × H) |
| 55. #365 | C2×C167 | semidirect |
| 56. #362 | C2×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #470×C167 | 2 |
| #430×C167 | 2 |
| #365×C167 | 2 |
| #362×C167 | 2 |
| #349×C167 | 2 |
| #2239 | 167 |