Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
856 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 856 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 | C23×C149 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C149 |
| prime radical | C23×D4×C149 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C149 ◁ C23×C4×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2646×C149 | C2 | semidirect |
| 4. #1294×C149 | C2 | semidirect |
| 5. #1280×C149 | C2 | semidirect |
| 187. #10344 | C149 | direct (N × H) |
| 188. C149 | #10344 | direct (N × H) |
| 189. #2646 | C2×C149 | semidirect |
| 192. #1294 | C2×C149 | semidirect |
| 193. #1280 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2646×C149 | 2 |
| #1786×C149 | 2 |
| #1438×C149 | 2 |
| #1294×C149 | 2 |
| #1280×C149 | 2 |
| #10344 | 149 |