Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
274 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C167 | #394 |
| commutator, Frattini, cosocle | C22×C4 | C23×C167 |
| prime radical | C2×AGL(1,ℤ/8)×C167 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C167 ◁ C22×C4×C167 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #430×C167 | C2 | semidirect |
| 3. #421×C167 | C2 | semidirect |
| 4. #418×C167 | C2 | semidirect |
| 5. #413×C167 | C2 | semidirect |
| 6. C2×#100×C167 | C2 | semidirect |
| 7. #344×C167 | C2 | semidirect |
| 110. C167 | #2048 | direct (N × H) |
| 111. #2048 | C167 | direct (N × H) |
| 113. #430 | C2×C167 | semidirect |
| 114. #421 | C2×C167 | semidirect |
| 115. #418 | C2×C167 | semidirect |
| 116. #413 | C2×C167 | semidirect |
| 117. C2×#100 | C2×C167 | semidirect |
| 118. #344 | C2×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,ℤ/8)×C167 | 2 |
| #430×C167 | 2 |
| #421×C167 | 2 |
| #418×C167 | 2 |
| #413×C167 | 2 |
| C2×#100×C167 | 2 |
| #344×C167 | 2 |
| #2048 | 167 |