Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
336 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C167 | C2×D4 |
| commutator | C2×C4 | C22×C4×C167 |
| Frattini, cosocle | C22×C4 | C23×C167 |
| socle | C22×C167 | C2×C22⋊C4 |
| prime radical | #532×C167 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C167 ◁ C2×C42×C167 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#104×C167 | C2 | semidirect |
| 3. C4×M16×C167 | C2 | semidirect |
| 4. C4×C4⋊C4×C167 | C2 | semidirect |
| 7. C4⋊Q8×C167 | C4 | semidirect |
| 8. #127×C167 | C4 | semidirect |
| 9. #124×C167 | C4 | semidirect |
| 34. M16×C167 | D4 | semidirect |
| 83. C4×C167 | #104 | semidirect |
| 92. C167 | #1980 | direct (N × H) |
| 93. #1980 | C167 | direct (N × H) |
| 95. C2×#104 | C2×C167 | semidirect |
| 96. C4×M16 | C2×C167 | semidirect |
| 97. C4×C4⋊C4 | C2×C167 | semidirect |
| 100. C4⋊Q8 | C4×C167 | semidirect |
| 101. #127 | C4×C167 | semidirect |
| 102. #124 | C4×C167 | semidirect |
| 127. M16 | D4×C167 | semidirect |
| 176. C4 | #104×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #532×C167 | 2 |
| C2×#104×C167 | 2 |
| C4×M16×C167 | 2 |
| C4×C4⋊C4×C167 | 2 |
| #1980 | 167 |