Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
1476 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1476 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D149 |
| commutator, socle, cosocle | C22×C149 | C25 |
| Fitting | C4×#41×C149 | C2 |
| hypercenter | C4×#41 | D149 |
| hypocenter | C149 | #3499 |
| LCS | G ▷ C22×C149 ▷ C149 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#18011958 | C2 | semidirect |
| 2. Q8×D596 | C2 | semidirect |
| 3. #23750279 | C2 | semidirect |
| 4. #23750201 | C2 | semidirect |
| 5. #23750175 | C2 | semidirect |
| 6. C2×#18011911 | C2 | semidirect |
| 7. C4×#41×C149 | C2 | semidirect |
| 42. #41×C149 | D4 | semidirect |
| 78. C4×C149 | 2−1+4 | semidirect |
| 84. C149 | #3499 | semidirect |
| 92. C4×#41 | D149 | semidirect |
| 115. #41 | D596 | semidirect |
| 164. C4 | #18011958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011958 | 2 |
| Q8×D596 | 2 |
| #23750279 | 2 |
| #23750201 | 2 |
| #23750175 | 2 |
| C2×#18011911 | 2 |
| C4×#41×C149 | 2 |
| #3499 | 149 |