Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
400 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C149 | #331 |
| commutator | C42 | C22×C4×C149 |
| Frattini, cosocle | C4×C8 | C23×C149 |
| socle | C2×C149 | C2×#331 |
| prime radical | #3147×C149 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C149 ◁ C22×C4×C149 ◁ C2×C4×C8×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#364×C149 | C2 | semidirect |
| 3. #1359×C149 | C2 | semidirect |
| 97. #11922 | C149 | direct (N × H) |
| 98. C149 | #11922 | direct (N × H) |
| 100. C2×#364 | C2×C149 | semidirect |
| 101. #1359 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3147×C149 | 2 |
| C2×#364×C149 | 2 |
| #1359×C149 | 2 |
| #11922 | 149 |