Finite Group DatabasebetaFinite Group DatabasebetaOrder 21184.
170 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C331 | C23 |
| commutator | C22 | C22×C4×C331 |
| Frattini, cosocle | C23 | C23×C331 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C331 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. C4⋊C4×C331 | C4 | semidirect |
| 42. C4×C331 | C4⋊C4 | semidirect |
| 50. C331 | #389 | direct (N × H) |
| 51. #389 | C331 | direct (N × H) |
| 64. C4⋊C4 | C4×C331 | semidirect |
| 93. C4 | C4⋊C4×C331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×C331 | 2 |
| C2×C42×C331 | 2 |
| #95×C331 | 2 |
| #389 | 331 |