Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#18012772 | C2 | semidirect |
| 3. C2×#18012718 | C2 | semidirect |
| 4. #23752376 | C2 | semidirect |
| 5. #23752370 | C2 | semidirect |
| 6. #23752365 | C2 | semidirect |
| 7. #23752214 | C2 | semidirect |
| 8. #407×C151 | C2 | semidirect |
| 15. C22×Dic302 | C22 | semidirect |
| 20. C2×Dic604 | C22 | semidirect |
| 21. C2×#14558993 | C22 | semidirect |
| 25. #18012718 | C22 | semidirect |
| 26. C2×C4⋊Dic151 | C22 | semidirect |
| 29. #18012664 | C22 | semidirect |
| 30. #18012661 | C22 | semidirect |
| 32. C2×M16×C151 | C22 | semidirect |
| 34. C22⋊C8×C151 | C22 | semidirect |
| 126. C22×C151 | #137 | semidirect |
| 146. C151 | #3007 | semidirect |
| 155. #407 | D151 | semidirect |
| 170. C2×M16 | C2×D151 | semidirect |
| 181. C22⋊C8 | C2×D151 | semidirect |
| 277. C22 | #18012772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14559004 | 2 |
| C2×#18012772 | 2 |
| C2×#18012718 | 2 |
| #23752376 | 2 |
| #23752370 | 2 |
| #23752365 | 2 |
| #23752214 | 2 |
| #407×C151 | 2 |
| #3007 | 151 |