Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
634 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 122 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×C149 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C149 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3245×C149 | C2 | semidirect |
| 2. #3036×C149 | C2 | semidirect |
| 3. #1954×C149 | C2 | semidirect |
| 4. #1492×C149 | C2 | semidirect |
| 5. #1292×C149 | C2 | semidirect |
| 66. C2×D4×C149 | D8 | semidirect |
| 162. #10254 | C149 | direct (N × H) |
| 163. C149 | #10254 | direct (N × H) |
| 164. #3245 | C2×C149 | semidirect |
| 165. #3036 | C2×C149 | semidirect |
| 166. #1954 | C2×C149 | semidirect |
| 167. #1492 | C2×C149 | semidirect |
| 168. #1292 | C2×C149 | semidirect |
| 229. C2×D4 | D8×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3245×C149 | 2 |
| #3036×C149 | 2 |
| #1954×C149 | 2 |
| #1492×C149 | 2 |
| #1292×C149 | 2 |
| #10254 | 149 |