Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
364 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 70 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×C4⋊C4 | C23×C149 |
| prime radical | #537×C149 | C22 |
| LCS | G ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C23×C149 ◁ C2×C4⋊C4×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #2789×C149 | C2 | semidirect |
| 5. #1354×C149 | C2 | semidirect |
| 6. #1346×C149 | C2 | semidirect |
| 7. #1324×C149 | C2 | semidirect |
| 172. #12143 | C149 | direct (N × H) |
| 173. C149 | #12143 | direct (N × H) |
| 174. #2789 | C2×C149 | semidirect |
| 178. #1354 | C2×C149 | semidirect |
| 179. #1346 | C2×C149 | semidirect |
| 180. #1324 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2789×C149 | 2 |
| #2040×C149 | 2 |
| #1610×C149 | 2 |
| #1604×C149 | 2 |
| #1354×C149 | 2 |
| #1346×C149 | 2 |
| #1324×C149 | 2 |
| #12143 | 149 |