Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
552 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 233 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D167 |
| commutator | C22×C167 | C23×C4 |
| Fitting | #382×C167 | C2 |
| socle, prime radical, cosocle | C23×C167 | C24 |
| hypercenter | #382 | D167 |
| hypocenter | C167 | #2351 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C4×Dic334 | C4 | semidirect |
| 48. Dic334 | C4⋊C4 | semidirect |
| 89. C167 | #2351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic334 | 2 |
| C2×#19128797 | 2 |
| #24923166 | 2 |
| #24923165 | 2 |
| #24923133 | 2 |
| C4×C4⋊Dic167 | 2 |
| #24923120 | 2 |
| #382×C167 | 2 |
| #2351 | 167 |