Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
296 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 296 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, socle | C22×C167 | #121 |
| commutator | C2×C4 | C22×C4×C167 |
| Frattini, cosocle | C22×C4 | C23×C167 |
| prime radical | C22×D4×C167 | C22 |
| LCS | G ▷ C2×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. C2×#108×C167 | C2 | semidirect |
| 3. #419×C167 | C2 | semidirect |
| 5. C2×#101×C167 | C2 | semidirect |
| 7. #405×C167 | C2 | semidirect |
| 13. C2×SD16×C167 | C4 | semidirect |
| 106. C167 | #1977 | direct (N × H) |
| 107. #1977 | C167 | direct (N × H) |
| 109. C2×#108 | C2×C167 | semidirect |
| 110. #419 | C2×C167 | semidirect |
| 112. C2×#101 | C2×C167 | semidirect |
| 114. #405 | C2×C167 | semidirect |
| 120. C2×SD16 | C4×C167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD16×C167 | 2 |
| C2×#108×C167 | 2 |
| #419×C167 | 2 |
| #418×C167 | 2 |
| C2×#101×C167 | 2 |
| C2×#100×C167 | 2 |
| #405×C167 | 2 |
| #1977 | 167 |