Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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×Q16×D151 | C2 | semidirect |
| 3. #23752450 | C2 | semidirect |
| 4. #23752419 | C2 | semidirect |
| 5. #23752366 | C2 | semidirect |
| 6. C4×Dic604 | C2 | semidirect |
| 8. #494×C151 | C2 | semidirect |
| 36. Dic604 | D4 | semidirect |
| 59. D604 | Q16 | semidirect |
| 78. C2×D151 | C2×Q16 | semidirect |
| 81. C4×C151 | C2×Q16 | semidirect |
| 91. C151 | D4×Q16 | semidirect |
| 95. #494 | D151 | semidirect |
| 176. C4 | Q16×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D151 | 2 |
| #23752877 | 2 |
| #23752450 | 2 |
| #23752419 | 2 |
| #23752366 | 2 |
| C4×Dic604 | 2 |
| C8×D604 | 2 |
| #494×C151 | 2 |
| D4×Q16 | 151 |