Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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×#18012767 | C2 | semidirect |
| 2. C2×#18012765 | C2 | semidirect |
| 3. C2×#18012735 | C2 | semidirect |
| 4. #23752680 | C2 | semidirect |
| 5. #23752411 | C2 | semidirect |
| 6. #23752406 | C2 | semidirect |
| 7. #23752235 | C2 | semidirect |
| 8. #23752216 | C2 | semidirect |
| 9. #418×C151 | C2 | semidirect |
| 15. C2×#14558993 | C22 | semidirect |
| 16. C2×#14558992 | C22 | semidirect |
| 17. C2×D1208 | C22 | semidirect |
| 18. C2×#14558989 | C22 | semidirect |
| 23. #18012704 | C22 | semidirect |
| 24. #18012701 | C22 | semidirect |
| 29. Dic151⋊C8 | C22 | semidirect |
| 30. #18012659 | C22 | semidirect |
| 34. #102×C151 | C22 | semidirect |
| 37. #14559004 | D4 | semidirect |
| 79. Dic302 | C2×D4 | semidirect |
| 84. D604 | C2×D4 | semidirect |
| 125. Dic151 | AGL(1,ℤ/8) | semidirect |
| 132. C151 | #3038 | semidirect |
| 142. #418 | D151 | semidirect |
| 167. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012767 | 2 |
| C2×#18012765 | 2 |
| C2×#18012735 | 2 |
| #23752680 | 2 |
| #23752411 | 2 |
| #23752406 | 2 |
| #23752235 | 2 |
| #23752216 | 2 |
| #418×C151 | 2 |
| #3038 | 151 |