Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
754 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 170 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 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C149 |
| prime radical | C2×#493×C149 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C149 ◁ C2×C42×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#486×C149 | C2 | semidirect |
| 3. #1957×C149 | C2 | semidirect |
| 4. #1956×C149 | C2 | semidirect |
| 5. #1273×C149 | C2 | semidirect |
| 134. #10307 | C149 | direct (N × H) |
| 135. C149 | #10307 | direct (N × H) |
| 137. C2×#486 | C2×C149 | semidirect |
| 138. #1957 | C2×C149 | semidirect |
| 139. #1956 | C2×C149 | semidirect |
| 140. #1273 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#493×C149 | 2 |
| C2×#486×C149 | 2 |
| #1957×C149 | 2 |
| #1956×C149 | 2 |
| #1273×C149 | 2 |
| #10307 | 149 |