Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
284 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C149 | #95 |
| commutator | C22×C4 | C42×C149 |
| Frattini, cosocle | C43 | C22×C149 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C149 ◁ C43×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 99. #7043 | C149 | direct (N × H) |
| 100. C149 | #7043 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1839×C149 | 2 |
| #1767×C149 | 2 |
| #1745×C149 | 2 |
| #7043 | 149 |