Finite Group DatabasebetaFinite Group DatabasebetaOrder 38144.
420 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C149 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C149 |
| prime radical | C22×D4×C149 | D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C149 ◁ C22×C4×C149 ◁ C2×C4×D4×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #1354×C149 | C2 | semidirect |
| 5. #1346×C149 | C2 | semidirect |
| 173. #11739 | C149 | direct (N × H) |
| 174. C149 | #11739 | direct (N × H) |
| 178. #1354 | C2×C149 | semidirect |
| 179. #1346 | C2×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2638×C149 | 2 |
| C4×#100×C149 | 2 |
| #1459×C149 | 2 |
| #1354×C149 | 2 |
| #1346×C149 | 2 |
| #11739 | 149 |