Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 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. #23752762 | C2 | semidirect |
| 2. #23752615 | C2 | semidirect |
| 3. #23752588 | C2 | semidirect |
| 4. #23752560 | C2 | semidirect |
| 5. #23752558 | C2 | semidirect |
| 6. #23752446 | C2 | semidirect |
| 7. C4×#14558989 | C2 | semidirect |
| 8. C2×C4×C151⋊C8 | C2 | semidirect |
| 9. #532×C151 | C2 | semidirect |
| 77. C151⋊C8 | #41 | semidirect |
| 89. C2×C4×C151 | D8 | semidirect |
| 120. C151 | #3169 | semidirect |
| 123. #532 | D151 | semidirect |
| 208. C2×C4 | #14558989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| #23752615 | 2 |
| #23752588 | 2 |
| #23752560 | 2 |
| #23752558 | 2 |
| #23752446 | 2 |
| C4×#14558989 | 2 |
| C2×C4×C151⋊C8 | 2 |
| #532×C151 | 2 |
| #3169 | 151 |