Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
696 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 155 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, socle, cosocle | C23×C167 | C24 |
| Fitting | #398×C167 | C2 |
| prime radical | #24923179 | C2 |
| hypercenter | #398 | D167 |
| hypocenter | C167 | #2392 |
| LCS | G ▷ C23×C167 ▷ C167 | |
| UCS | C1 ◁ C23 ◁ #398 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19128794 | C2 | semidirect |
| 2. C2×#19128794 | C2 | semidirect |
| 3. C2×#19128790 | C2 | semidirect |
| 4. #24923195 | C2 | semidirect |
| 5. #24923191 | C2 | semidirect |
| 6. #24923187 | C2 | semidirect |
| 7. #24923186 | C2 | semidirect |
| 9. #24923120 | C2 | semidirect |
| 10. #24923116 | C2 | semidirect |
| 11. #398×C167 | C2 | semidirect |
| 54. C2×C4×D167 | D4 | semidirect |
| 66. C4×Dic167 | D4 | semidirect |
| 148. C167 | #2392 | semidirect |
| 153. #398 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128794 | 2 |
| C2×#19128790 | 2 |
| #24923195 | 2 |
| #24923191 | 2 |
| #24923187 | 2 |
| #24923186 | 2 |
| #24923179 | 2 |
| #24923120 | 2 |
| #24923116 | 2 |
| #398×C167 | 2 |
| #2392 | 167 |