Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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×#18012680 | C2 | semidirect |
| 2. C2×C16×D151 | C2 | semidirect |
| 3. #23752449 | C2 | semidirect |
| 4. #23752445 | C2 | semidirect |
| 5. #23752037 | C2 | semidirect |
| 6. #23752014 | C2 | semidirect |
| 7. #357×C151 | C2 | semidirect |
| 33. C151⋊C16 | D4 | semidirect |
| 67. C2×D151 | D16 | semidirect |
| 79. C151 | #2215 | semidirect |
| 87. #357 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012680 | 2 |
| C2×C16×D151 | 2 |
| #23752449 | 2 |
| #23752445 | 2 |
| #23752037 | 2 |
| #23752014 | 2 |
| #357×C151 | 2 |
| #2215 | 151 |