Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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 | #401×C149 | C2 |
| prime radical | C23×D149 | C23 |
| hypercenter | #401 | D149 |
| hypocenter | C149 | #2834 |
| LCS | G ▷ C23×C149 ▷ C149 | |
| UCS | C1 ◁ C23 ◁ #401 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C149⋊#401 | C2 | semidirect |
| 3. #23749559 | C2 | semidirect |
| 4. #23749557 | C2 | semidirect |
| 7. #401×C149 | C2 | semidirect |
| 69. C149 | #2834 | semidirect |
| 72. #401 | D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C149⋊#401 | 2 |
| #23749562 | 2 |
| #23749559 | 2 |
| #23749557 | 2 |
| #23749554 | 2 |
| #23749499 | 2 |
| #401×C149 | 2 |
| #2834 | 149 |