Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 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. #23752760 | C2 | semidirect |
| 2. #23752617 | C2 | semidirect |
| 3. #23752558 | C2 | semidirect |
| 4. #23752445 | C2 | semidirect |
| 5. D8×Dic151 | C2 | semidirect |
| 6. C4×C8×D151 | C2 | semidirect |
| 7. #493×C151 | C2 | semidirect |
| 56. C4×D151 | D8 | semidirect |
| 65. C8×C151 | #41 | semidirect |
| 85. C151 | #3169 | semidirect |
| 89. #493 | D151 | semidirect |
| 151. C8 | #14559003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752760 | 2 |
| #23752617 | 2 |
| #23752558 | 2 |
| #23752445 | 2 |
| D8×Dic151 | 2 |
| C4×C8×D151 | 2 |
| #493×C151 | 2 |
| #3169 | 151 |