Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
572 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 145 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×#18012758 | C2 | semidirect |
| 2. #23752760 | C2 | semidirect |
| 3. #23752595 | C2 | semidirect |
| 4. #23752592 | C2 | semidirect |
| 5. #23752584 | C2 | semidirect |
| 6. C4×C8×D151 | C2 | semidirect |
| 7. #493×C151 | C2 | semidirect |
| 32. C8×D151 | D4 | semidirect |
| 63. C4×C151 | #135 | semidirect |
| 72. C151 | #3147 | semidirect |
| 78. #493 | D151 | semidirect |
| 139. C4 | #18012758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012758 | 2 |
| #23752760 | 2 |
| #23752595 | 2 |
| #23752592 | 2 |
| #23752584 | 2 |
| C4×C8×D151 | 2 |
| #493×C151 | 2 |
| #3147 | 151 |