Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
696 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 151 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 | #397×C167 | C2 |
| prime radical | #24923178 | C2 |
| hypercenter | #397 | D167 |
| hypocenter | C167 | #2392 |
| LCS | G ▷ C23×C167 ▷ C167 | |
| UCS | C1 ◁ C23 ◁ #397 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19128794 | C2 | semidirect |
| 2. C2×(C22⋊D167)⋊C4 | C2 | semidirect |
| 3. C2×#19128788 | C2 | semidirect |
| 4. #24923200 | C2 | semidirect |
| 5. #24923193 | C2 | semidirect |
| 6. #24923187 | C2 | semidirect |
| 7. #24923184 | C2 | semidirect |
| 9. #24923120 | C2 | semidirect |
| 10. #24923116 | C2 | semidirect |
| 11. #397×C167 | C2 | semidirect |
| 46. C22×Dic167 | D4 | semidirect |
| 66. C4×Dic167 | D4 | semidirect |
| 148. C167 | #2392 | semidirect |
| 154. #397 | 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×(C22⋊D167)⋊C4 | 2 |
| C2×#19128788 | 2 |
| #24923200 | 2 |
| #24923193 | 2 |
| #24923187 | 2 |
| #24923184 | 2 |
| #24923178 | 2 |
| #24923120 | 2 |
| #24923116 | 2 |
| #397×C167 | 2 |
| #2392 | 167 |