Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
460 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 205 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 | C22×C149 | C23×C4 |
| Fitting | #376×C149 | C2 |
| socle, prime radical, cosocle | C23×C149 | C24 |
| hypercenter | #376 | D149 |
| hypocenter | C149 | #2331 |
| LCS | G ▷ C22×C149 ▷ C149 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #18011911 | C4 | semidirect |
| 40. C42×C149 | Q8 | semidirect |
| 79. C149 | #2331 | semidirect |
| 120. C42 | Dic298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011911 | 2 |
| #23749529 | 2 |
| #23749523 | 2 |
| #23749508 | 2 |
| #23749491 | 2 |
| C4×C4⋊Dic149 | 2 |
| #376×C149 | 2 |
| #2331 | 149 |