Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
278 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 84 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, Frattini, cosocle | C22×C4 | C23×C167 |
| prime radical | C2×#41×C167 | C22 |
| LCS | G ▷ C22×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. #428×C167 | C2 | semidirect |
| 5. C2×#101×C167 | C2 | semidirect |
| 6. #391×C167 | C2 | semidirect |
| 7. #339×C167 | C2 | semidirect |
| 120. C167 | #2038 | direct (N × H) |
| 121. #2038 | C167 | direct (N × H) |
| 123. #428 | C2×C167 | semidirect |
| 126. C2×#101 | C2×C167 | semidirect |
| 127. #391 | C2×C167 | semidirect |
| 128. #339 | C2×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #536×C167 | 2 |
| #428×C167 | 2 |
| C2×#104×C167 | 2 |
| #417×C167 | 2 |
| C2×#101×C167 | 2 |
| #391×C167 | 2 |
| #339×C167 | 2 |
| #2038 | 167 |