Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D149 |
| commutator, socle, cosocle | C23×C149 | C24 |
| Fitting | #396×C149 | C2 |
| prime radical | C24×D149 | C22 |
| hypercenter | #396 | D149 |
| hypocenter | C149 | #2842 |
| LCS | G ▷ C23×C149 ▷ C149 | |
| UCS | C1 ◁ C23 ◁ #396 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23749562 | C2 | semidirect |
| 2. #23749560 | C2 | semidirect |
| 3. #23749549 | C2 | semidirect |
| 4. #23749548 | C2 | semidirect |
| 5. #23749547 | C2 | semidirect |
| 7. #396×C149 | C2 | semidirect |
| 9. C2×C4⋊Dic149 | C22 | semidirect |
| 10. C2×#14558715 | C22 | semidirect |
| 11. C2×#14558715 | C22 | semidirect |
| 17. #18011818 | C22 | semidirect |
| 18. C2×C4⋊C4×C149 | C22 | semidirect |
| 20. #95×C149 | C22 | semidirect |
| 89. C149 | #2842 | semidirect |
| 96. #396 | D149 | semidirect |
| 102. C2×C4⋊C4 | C2×D149 | semidirect |
| 110. #95 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23749562 | 2 |
| #23749560 | 2 |
| #23749549 | 2 |
| #23749548 | 2 |
| #23749547 | 2 |
| #23749480 | 2 |
| #396×C149 | 2 |
| #2842 | 149 |