Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012786 | C2 | semidirect |
| 2. C2×#18012764 | C2 | semidirect |
| 3. C22×#14558993 | C2 | semidirect |
| 4. #23752781 | C2 | semidirect |
| 5. #23752358 | C2 | semidirect |
| 6. #23752352 | C2 | semidirect |
| 7. #23752220 | C2 | semidirect |
| 8. #23752178 | C2 | semidirect |
| 9. #416×C151 | C2 | semidirect |
| 15. C2×#14559003 | C22 | semidirect |
| 18. C2×Q8×D151 | C22 | semidirect |
| 30. #18012662 | C22 | semidirect |
| 31. (C2×D151)⋊C8 | C22 | semidirect |
| 35. #103×C151 | C22 | semidirect |
| 36. #102×C151 | C22 | semidirect |
| 49. C2×Dic302 | D4 | semidirect |
| 72. #41×C151 | D4 | semidirect |
| 145. C151 | #3010 | semidirect |
| 154. #416 | D151 | semidirect |
| 180. #103 | C2×D151 | semidirect |
| 181. #102 | C2×D151 | semidirect |
| 191. #41 | D604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012786 | 2 |
| C2×#18012764 | 2 |
| C22×#14558993 | 2 |
| #23752781 | 2 |
| #23752358 | 2 |
| #23752352 | 2 |
| #23752220 | 2 |
| #23752178 | 2 |
| #416×C151 | 2 |
| #3010 | 151 |