Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. #23752109 | C2 | semidirect |
| 4. #23752106 | C2 | semidirect |
| 5. #23752100 | C2 | semidirect |
| 6. #23752094 | C2 | semidirect |
| 7. #23752085 | C2 | semidirect |
| 8. #23752070 | C2 | semidirect |
| 11. #18012720 | C4 | semidirect |
| 34. C22×Dic151 | C2×C4 | semidirect |
| 43. Dic151⋊C4 | C2×C4 | semidirect |
| 47. C22⋊Dic151 | C2×C4 | semidirect |
| 126. C151 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012720 | 2 |
| #23752115 | 2 |
| #23752109 | 2 |
| #23752106 | 2 |
| #23752100 | 2 |
| #23752094 | 2 |
| #23752085 | 2 |
| #23752070 | 2 |
| #386×C151 | 2 |
| #2376 | 151 |