Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #23752680 | C2 | semidirect |
| 3. #23752228 | C2 | semidirect |
| 4. C2×#18012665 | C2 | semidirect |
| 5. #23752185 | C2 | semidirect |
| 6. #23751973 | C2 | semidirect |
| 7. #344×C151 | C2 | semidirect |
| 11. #18012772 | C4 | semidirect |
| 13. #18012767 | C4 | semidirect |
| 37. C2×Dic302 | C2×C4 | semidirect |
| 39. C2×D604 | C2×C4 | semidirect |
| 64. M16×C151 | C2×C4 | semidirect |
| 129. C151 | #1906 | semidirect |
| 136. #344 | D151 | semidirect |
| 185. M16 | C4×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753012 | 2 |
| #23752680 | 2 |
| #23752228 | 2 |
| C2×#18012665 | 2 |
| #23752185 | 2 |
| #23751973 | 2 |
| #344×C151 | 2 |
| #1906 | 151 |