Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23753010 | C2 | semidirect |
| 2. C2×#18012767 | C2 | semidirect |
| 3. #23752776 | C2 | semidirect |
| 4. #23752216 | C2 | semidirect |
| 5. #23752185 | C2 | semidirect |
| 6. #23751984 | C2 | semidirect |
| 7. #421×C151 | C2 | semidirect |
| 36. C2×Dic302 | D4 | semidirect |
| 43. C2×D604 | D4 | semidirect |
| 55. C2×C151⋊C8 | D4 | semidirect |
| 70. M16×C151 | D4 | semidirect |
| 142. C151 | #2008 | semidirect |
| 147. #421 | D151 | semidirect |
| 208. M16 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753010 | 2 |
| C2×#18012767 | 2 |
| #23752776 | 2 |
| #23752216 | 2 |
| #23752185 | 2 |
| #23751984 | 2 |
| #421×C151 | 2 |
| #2008 | 151 |