Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14558994 | C2 | semidirect |
| 3. #23752591 | C2 | semidirect |
| 4. #23752451 | C2 | semidirect |
| 5. #23752422 | C2 | semidirect |
| 6. #23752419 | C2 | semidirect |
| 7. #23752368 | C2 | semidirect |
| 8. #23752367 | C2 | semidirect |
| 9. C4×#14558994 | C2 | semidirect |
| 52. #14558994 | D4 | direct (N × H) |
| 100. D4×C151 | Q16 | semidirect |
| 113. C22×C151 | C2×Q16 | semidirect |
| 120. C4×C151 | C2×Q16 | semidirect |
| 130. C151 | D4×Q16 | semidirect |
| 224. D4 | #14558994 | direct (N × H) |
| 244. C22 | C2×#14558994 | semidirect |
| 254. C4 | C2×#14558994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558994 | 2 |
| D4×Dic302 | 2 |
| #23752591 | 2 |
| #23752451 | 2 |
| #23752422 | 2 |
| #23752419 | 2 |
| #23752368 | 2 |
| #23752367 | 2 |
| C4×#14558994 | 2 |
| D4×C151⋊C8 | 2 |
| D4×Q8×C151 | 2 |
| D4×Q16 | 151 |