Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
376 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C149 | C2×D4 |
| commutator | C2×C4 | C22×C4×C149 |
| Frattini, cosocle | C22×C4 | C23×C149 |
| socle | C22×C149 | C2×C22⋊C4 |
| prime radical | #525×C149 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C149 ◁ C23×C4×C149 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×M16×C149 | C2 | semidirect |
| 3. C2×#104×C149 | C2 | semidirect |
| 4. C4×C22⋊C4×C149 | C2 | semidirect |
| 5. #339×C149 | C2 | semidirect |
| 13. C22⋊Q8×C149 | C4 | semidirect |
| 14. C22⋊Q8×C149 | C4 | semidirect |
| 15. #121×C149 | C4 | semidirect |
| 16. #121×C149 | C4 | semidirect |
| 45. M16×C149 | D4 | semidirect |
| 106. C22×C149 | #104 | semidirect |
| 125. C149 | #1871 | direct (N × H) |
| 126. #1871 | C149 | direct (N × H) |
| 127. C22×M16 | C2×C149 | semidirect |
| 129. C2×#104 | C2×C149 | semidirect |
| 130. C4×C22⋊C4 | C2×C149 | semidirect |
| 131. #339 | C2×C149 | semidirect |
| 139. C22⋊Q8 | C4×C149 | semidirect |
| 140. C22⋊Q8 | C4×C149 | semidirect |
| 141. #121 | C4×C149 | semidirect |
| 142. #121 | C4×C149 | semidirect |
| 171. M16 | D4×C149 | semidirect |
| 232. C22 | #104×C149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×M16×C149 | 2 |
| #525×C149 | 2 |
| C2×#104×C149 | 2 |
| C4×C22⋊C4×C149 | 2 |
| #339×C149 | 2 |
| #1871 | 149 |