Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
592 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 592 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 | C2×C4 | C22×C4×C167 |
| Frattini, cosocle | C22×C4 | C23×C167 |
| prime radical | C24×C167 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C167 ◁ C23×C4×C167 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#103×C167 | C2 | semidirect |
| 8. C22×Q8×C167 | C4 | semidirect |
| 49. Q8×C167 | C22⋊C4 | semidirect |
| 68. C22×C167 | #103 | semidirect |
| 85. C167 | #1787 | direct (N × H) |
| 86. #1787 | C167 | direct (N × H) |
| 88. C2×#103 | C2×C167 | semidirect |
| 94. C22×Q8 | C4×C167 | semidirect |
| 135. Q8 | C22⋊C4×C167 | semidirect |
| 154. C22 | #103×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×C167 | 2 |
| C2×#103×C167 | 2 |
| C2×C22⋊C8×C167 | 2 |
| #380×C167 | 2 |
| #1787 | 167 |