Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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. #23753026 | C2 | semidirect |
| 2. C2×#18012683 | C2 | semidirect |
| 3. #23752479 | C2 | semidirect |
| 4. #23752029 | C2 | semidirect |
| 5. #23752019 | C2 | semidirect |
| 6. #23751997 | C2 | semidirect |
| 7. #509×C151 | C2 | semidirect |
| 90. C151 | #2193 | semidirect |
| 93. #509 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753026 | 2 |
| C2×#18012683 | 2 |
| #23752479 | 2 |
| #23752029 | 2 |
| #23752019 | 2 |
| #23751997 | 2 |
| #509×C151 | 2 |
| #2193 | 151 |