Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 1. C2×#18012761 | C2 | semidirect |
| 2. #23752642 | C2 | direct (N × H) |
| 3. C2×#18012685 | C2 | semidirect |
| 4. C2×#18012683 | C2 | semidirect |
| 5. C2×#18012682 | C2 | semidirect |
| 6. C2×#18012680 | C2 | semidirect |
| 7. C22×C151⋊C16 | C2 | semidirect |
| 8. C2×#135×C151 | C2 | semidirect |
| 11. #18012761 | C22 | semidirect |
| 15. #18012685 | C22 | semidirect |
| 16. #18012683 | C22 | semidirect |
| 17. #18012682 | C22 | semidirect |
| 18. #18012680 | C22 | semidirect |
| 21. C2×C151⋊C16 | C22 | semidirect |
| 24. #135×C151 | C22 | semidirect |
| 96. C2×C151 | #508 | semidirect |
| 99. C151 | C2×#508 | semidirect |
| 102. C2×#135 | D151 | semidirect |
| 114. #135 | C2×D151 | semidirect |
| 197. C2 | #23752642 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012761 | 2 |
| #23752642 | 2 |
| C2×#18012685 | 2 |
| C2×#18012683 | 2 |
| C2×#18012682 | 2 |
| C2×#18012680 | 2 |
| C22×C151⋊C16 | 2 |
| C2×#135×C151 | 2 |
| C2×#508 | 151 |