Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23752824 | C2 | semidirect |
| 3. #23752554 | C2 | semidirect |
| 4. #23752513 | C2 | semidirect |
| 5. #23752418 | C2 | semidirect |
| 7. #23752314 | C2 | semidirect |
| 8. C4×#14558993 | C2 | semidirect |
| 9. #433×C151 | C2 | semidirect |
| 13. #18012739 | C22 | semidirect |
| 15. #18012731 | C22 | semidirect |
| 18. C4×Dic302 | C22 | semidirect |
| 24. #18012673 | C22 | semidirect |
| 25. #18012671 | C22 | semidirect |
| 26. #18012664 | C22 | semidirect |
| 27. #18012664 | C22 | semidirect |
| 31. C4⋊C8×C151 | C22 | semidirect |
| 33. #97×C151 | C22 | semidirect |
| 34. C4×C8×C151 | C22 | semidirect |
| 102. C151 | #3123 | semidirect |
| 112. #433 | D151 | semidirect |
| 130. C4⋊C8 | C2×D151 | semidirect |
| 136. #97 | C2×D151 | semidirect |
| 137. C4×C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752824 | 2 |
| #23752686 | 2 |
| #23752554 | 2 |
| #23752513 | 2 |
| #23752418 | 2 |
| #23752365 | 2 |
| #23752314 | 2 |
| C4×#14558993 | 2 |
| #433×C151 | 2 |
| #3123 | 151 |