Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
336 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23752847 | C2 | semidirect |
| 2. #23752404 | C2 | semidirect |
| 3. #23751956 | C2 | semidirect |
| 4. #23751941 | C2 | semidirect |
| 5. #493×C151 | C2 | semidirect |
| 11. C4⋊(C151⋊C8) | C22 | semidirect |
| 15. #127×C151 | C22 | semidirect |
| 16. C4×C8×C151 | C22 | semidirect |
| 39. D604 | D8 | semidirect |
| 74. C151 | #1619 | semidirect |
| 77. #493 | D151 | semidirect |
| 85. #127 | C2×D151 | semidirect |
| 91. C4×C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752847 | 2 |
| #23752404 | 2 |
| #23751956 | 2 |
| #23751941 | 2 |
| #493×C151 | 2 |
| #1619 | 151 |