Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23752695 | C2 | semidirect |
| 3. #23752537 | C2 | semidirect |
| 4. #23752537 | C2 | semidirect |
| 5. #23752531 | C2 | semidirect |
| 6. #23752526 | C2 | semidirect |
| 7. #23752254 | C2 | semidirect |
| 8. #23752250 | C2 | semidirect |
| 9. #23752218 | C2 | semidirect |
| 10. C2×#18012661 | C2 | semidirect |
| 11. #408×C151 | C2 | semidirect |
| 23. #18012698 | C22 | semidirect |
| 25. C2×C4⋊Dic151 | 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. C22⋊C8×C151 | C22 | semidirect |
| 40. C22⋊C8×C151 | C22 | semidirect |
| 134. C151 | #3096 | semidirect |
| 146. #408 | D151 | semidirect |
| 174. C22⋊C8 | C2×D151 | semidirect |
| 175. C22⋊C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752776 | 2 |
| #23752695 | 2 |
| #23752537 | 2 |
| #23752531 | 2 |
| #23752526 | 2 |
| #23752254 | 2 |
| #23752250 | 2 |
| #23752218 | 2 |
| C2×#18012661 | 2 |
| #408×C151 | 2 |
| #3096 | 151 |