Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#18012738 | C2 | semidirect |
| 3. #23752506 | C2 | semidirect |
| 4. #23752501 | C2 | semidirect |
| 5. #23752496 | C2 | semidirect |
| 6. #23752491 | C2 | semidirect |
| 7. #23752255 | C2 | semidirect |
| 8. #23752235 | C2 | semidirect |
| 11. #428×C151 | C2 | semidirect |
| 44. #14559004 | Q8 | semidirect |
| 87. Dic302 | C2×Q8 | semidirect |
| 89. D604 | C2×Q8 | semidirect |
| 138. C151 | #3079 | semidirect |
| 147. #428 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012738 | 2 |
| #23752680 | 2 |
| #23752506 | 2 |
| #23752501 | 2 |
| #23752496 | 2 |
| #23752491 | 2 |
| #23752255 | 2 |
| #23752235 | 2 |
| #23752214 | 2 |
| #23752211 | 2 |
| #428×C151 | 2 |
| #3079 | 151 |