Finite Group DatabasebetaFinite Group DatabasebetaOrder 1216.
294 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 103 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 | C23×D19 |
| commutator, socle, cosocle | C22×C19 | C24 |
| Fitting | C19×C22⋊Q8 | C2 |
| hypercenter | C22⋊Q8 | D19 |
| hypocenter | C19 | #537 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64545 | C2 | semidirect |
| 2. C2×#64541 | C2 | semidirect |
| 3. C19×C22⋊Q8 | C2 | semidirect |
| 4. #10597392 | C2 | semidirect |
| 5. #10597376 | C2 | semidirect |
| 6. #10597342 | C2 | semidirect |
| 7. #10597341 | C2 | semidirect |
| 8. #10597341 | C2 | semidirect |
| 9. C4⋊C4×D19 | C2 | semidirect |
| 10. #10597330 | C2 | semidirect |
| 11. #10597330 | C2 | semidirect |
| 60. C4×D19 | D4 | semidirect |
| 94. C22⋊Q8 | D19 | semidirect |
| 101. C19 | #537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64545 | 2 |
| C2×#64541 | 2 |
| C19×C22⋊Q8 | 2 |
| #10597392 | 2 |
| #10597376 | 2 |
| #10597342 | 2 |
| #10597341 | 2 |
| C4⋊C4×D19 | 2 |
| #10597330 | 2 |
| #537 | 19 |