Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23752840 | C2 | semidirect |
| 3. #23752513 | C2 | semidirect |
| 4. #23752513 | C2 | semidirect |
| 5. #23752503 | C2 | semidirect |
| 6. #23752493 | C2 | semidirect |
| 7. #23752254 | C2 | semidirect |
| 8. #23752250 | C2 | semidirect |
| 11. #424×C151 | C2 | semidirect |
| 13. #18012739 | C22 | semidirect |
| 15. #18012731 | C22 | semidirect |
| 26. #18012673 | C22 | semidirect |
| 27. #18012673 | C22 | semidirect |
| 28. #18012673 | C22 | semidirect |
| 29. #18012671 | C22 | semidirect |
| 30. #18012671 | C22 | semidirect |
| 31. #18012671 | C22 | semidirect |
| 39. C4⋊C8×C151 | C22 | semidirect |
| 40. C4⋊C8×C151 | C22 | semidirect |
| 45. C2×D604 | Q8 | semidirect |
| 124. C151 | #3081 | semidirect |
| 134. #424 | D151 | semidirect |
| 160. C4⋊C8 | C2×D151 | semidirect |
| 161. C4⋊C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752840 | 2 |
| #23752686 | 2 |
| #23752513 | 2 |
| #23752503 | 2 |
| #23752493 | 2 |
| #23752254 | 2 |
| #23752250 | 2 |
| #23752218 | 2 |
| C2×#18012661 | 2 |
| #424×C151 | 2 |
| #3081 | 151 |