Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
388 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 168 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 | C4 | C2×C42×C167 |
| Frattini, cosocle | C22×C4 | C23×C167 |
| prime radical | C22×D4×C167 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C167 ◁ C2×C42×C167 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#97×C167 | C2 | semidirect |
| 4. C4×C4⋊C4×C167 | C2 | semidirect |
| 5. #340×C167 | C2 | semidirect |
| 10. C4×D4×C167 | C4 | semidirect |
| 16. #102×C167 | C4 | semidirect |
| 33. C2×C8×C167 | C2×C4 | semidirect |
| 37. C4⋊C4×C167 | C2×C4 | semidirect |
| 50. D4×C167 | C42 | semidirect |
| 90. C167 | #1762 | direct (N × H) |
| 91. #1762 | C167 | direct (N × H) |
| 94. C2×#97 | C2×C167 | semidirect |
| 95. C4×C4⋊C4 | C2×C167 | semidirect |
| 96. #340 | C2×C167 | semidirect |
| 101. C4×D4 | C4×C167 | semidirect |
| 107. #102 | C4×C167 | semidirect |
| 124. C2×C8 | C2×C4×C167 | semidirect |
| 128. C4⋊C4 | C2×C4×C167 | semidirect |
| 141. D4 | C42×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C167 | 2 |
| C2×#102×C167 | 2 |
| C2×#97×C167 | 2 |
| C4×C4⋊C4×C167 | 2 |
| #340×C167 | 2 |
| #1762 | 167 |