Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
444 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C167 | #120 |
| commutator | C2×C4 | C22×C4×C167 |
| Frattini, cosocle | C22×C4 | C23×C167 |
| prime radical | C2×#127×C167 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C167 ◁ C22×C4×C167 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #518×C167 | C2 | semidirect |
| 3. #418×C167 | C2 | semidirect |
| 4. C2×#100×C167 | C2 | semidirect |
| 5. #339×C167 | C2 | semidirect |
| 11. #127×C167 | C4 | semidirect |
| 28. C2×D4×C167 | C2×C4 | semidirect |
| 36. C4⋊C4×C167 | D4 | semidirect |
| 41. C42×C167 | C2×C4 | semidirect |
| 87. C167 | #1887 | direct (N × H) |
| 88. #1887 | C167 | direct (N × H) |
| 90. #518 | C2×C167 | semidirect |
| 91. #418 | C2×C167 | semidirect |
| 92. C2×#100 | C2×C167 | semidirect |
| 93. #339 | C2×C167 | semidirect |
| 99. #127 | C4×C167 | semidirect |
| 116. C2×D4 | C2×C4×C167 | semidirect |
| 124. C4⋊C4 | D4×C167 | semidirect |
| 129. C42 | C2×C4×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#127×C167 | 2 |
| #518×C167 | 2 |
| #418×C167 | 2 |
| C2×#100×C167 | 2 |
| #339×C167 | 2 |
| #1887 | 167 |