Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
368 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C167 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C167 |
| prime radical | C2×#121×C167 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C167 ◁ C23×C4×C167 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#106×C167 | C2 | semidirect |
| 3. C2×#102×C167 | C2 | semidirect |
| 4. C2×#102×C167 | C2 | semidirect |
| 5. C2×C22⋊C8×C167 | C2 | semidirect |
| 6. #380×C167 | C2 | semidirect |
| 7. #340×C167 | C2 | semidirect |
| 52. C2×C8×C167 | D4 | semidirect |
| 143. C167 | #2034 | direct (N × H) |
| 144. #2034 | C167 | direct (N × H) |
| 146. C2×#106 | C2×C167 | semidirect |
| 147. C2×#102 | C2×C167 | semidirect |
| 148. C2×#102 | C2×C167 | semidirect |
| 149. C2×C22⋊C8 | C2×C167 | semidirect |
| 150. #380 | C2×C167 | semidirect |
| 151. #340 | C2×C167 | semidirect |
| 196. C2×C8 | D4×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#121×C167 | 2 |
| C2×#106×C167 | 2 |
| C2×#102×C167 | 2 |
| C2×C22⋊C8×C167 | 2 |
| #380×C167 | 2 |
| #340×C167 | 2 |
| #2034 | 167 |