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×#18012770 | C2 | semidirect |
| 3. #23752591 | C2 | semidirect |
| 4. #23752468 | C2 | semidirect |
| 5. #23752422 | C2 | semidirect |
| 6. #23752414 | C2 | semidirect |
| 7. #23752372 | C2 | semidirect |
| 8. #23752368 | C2 | semidirect |
| 9. C4×#14558991 | C2 | semidirect |
| 10. #23752290 | C2 | semidirect |
| 11. D4×Q8×C151 | C2 | semidirect |
| 53. #14558991 | D4 | semidirect |
| 124. C4×C151 | #137 | semidirect |
| 134. C151 | #3276 | semidirect |
| 137. D4×Q8 | D151 | semidirect |
| 261. C4 | #18012770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012770 | 2 |
| #23752867 | 2 |
| #23752591 | 2 |
| #23752468 | 2 |
| #23752422 | 2 |
| #23752414 | 2 |
| #23752372 | 2 |
| #23752368 | 2 |
| C4×#14558991 | 2 |
| #23752290 | 2 |
| D4×Q8×C151 | 2 |
| #3276 | 151 |