Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
300 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 300 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 | C2×C4×C167 | C2×D4 |
| commutator | C2×C4 | C22×C4×C167 |
| Frattini, cosocle | C22×C4 | C23×C167 |
| socle | C22×C167 | C4×D4 |
| prime radical | C2×#135×C167 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C167 ◁ C22×C8×C167 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#108×C167 | C2 | semidirect |
| 3. C2×#104×C167 | C2 | semidirect |
| 4. #408×C167 | C2 | semidirect |
| 5. C2×C4×C8×C167 | C2 | semidirect |
| 9. C2×Q16×C167 | C4 | semidirect |
| 10. C2×SD16×C167 | C4 | semidirect |
| 11. C2×D8×C167 | C4 | semidirect |
| 85. C167 | #1974 | direct (N × H) |
| 86. #1974 | C167 | direct (N × H) |
| 88. C2×#108 | C2×C167 | semidirect |
| 89. C2×#104 | C2×C167 | semidirect |
| 90. #408 | C2×C167 | semidirect |
| 91. C2×C4×C8 | C2×C167 | semidirect |
| 95. C2×Q16 | C4×C167 | semidirect |
| 96. C2×SD16 | C4×C167 | semidirect |
| 97. C2×D8 | C4×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#135×C167 | 2 |
| C2×#108×C167 | 2 |
| C2×#104×C167 | 2 |
| #408×C167 | 2 |
| C2×C4×C8×C167 | 2 |
| #1974 | 167 |