Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23753017 | C2 | semidirect |
| 2. #23752653 | C2 | semidirect |
| 3. #23752647 | C2 | semidirect |
| 4. #23752642 | C2 | semidirect |
| 5. C2×#18012682 | C2 | semidirect |
| 6. #23752629 | C2 | semidirect |
| 7. #578×C151 | C2 | semidirect |
| 12. #18012685 | C22 | semidirect |
| 13. #18012683 | C22 | semidirect |
| 14. #18012682 | C22 | semidirect |
| 15. #18012682 | C22 | semidirect |
| 16. #18012680 | C22 | semidirect |
| 17. #18012679 | C22 | semidirect |
| 18. C2×C151⋊C16 | C22 | semidirect |
| 21. #135×C151 | C22 | semidirect |
| 22. C2×Q16×C151 | C22 | semidirect |
| 74. C151 | #3416 | semidirect |
| 76. #578 | D151 | semidirect |
| 88. #135 | C2×D151 | semidirect |
| 89. C2×Q16 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753017 | 2 |
| #23752653 | 2 |
| #23752647 | 2 |
| #23752642 | 2 |
| C2×#18012682 | 2 |
| #23752629 | 2 |
| #578×C151 | 2 |
| #3416 | 151 |