Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
254 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C167 | #394 |
| commutator, Frattini, cosocle | C22×C4 | C23×C167 |
| prime radical | C2×#41×C167 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C167 ◁ C22×C4×C167 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #430×C167 | C2 | semidirect |
| 4. #419×C167 | C2 | semidirect |
| 6. C2×#101×C167 | C2 | semidirect |
| 7. #344×C167 | C2 | semidirect |
| 105. C167 | #2049 | direct (N × H) |
| 106. #2049 | C167 | direct (N × H) |
| 108. #430 | C2×C167 | semidirect |
| 110. #419 | C2×C167 | semidirect |
| 112. C2×#101 | C2×C167 | semidirect |
| 113. #344 | C2×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#137×C167 | 2 |
| #430×C167 | 2 |
| #421×C167 | 2 |
| #419×C167 | 2 |
| #413×C167 | 2 |
| C2×#101×C167 | 2 |
| #344×C167 | 2 |
| #2049 | 167 |