Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#18012730 | C2 | semidirect |
| 3. #23752522 | C2 | semidirect |
| 4. #23752518 | C2 | semidirect |
| 5. #23752515 | C2 | semidirect |
| 6. #23752511 | C2 | semidirect |
| 7. #23752255 | C2 | semidirect |
| 8. #23752235 | C2 | semidirect |
| 11. #428×C151 | C2 | semidirect |
| 135. C151 | #3080 | semidirect |
| 144. #428 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012730 | 2 |
| #23752680 | 2 |
| #23752522 | 2 |
| #23752518 | 2 |
| #23752515 | 2 |
| #23752511 | 2 |
| #23752255 | 2 |
| #23752235 | 2 |
| #23752214 | 2 |
| #23752211 | 2 |
| #428×C151 | 2 |
| #3080 | 151 |