Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 3. #23752620 | C2 | semidirect |
| 4. #23752619 | C2 | semidirect |
| 5. #23752613 | C2 | semidirect |
| 6. #23752612 | C2 | semidirect |
| 48. #14558988 | Q8 | semidirect |
| 72. M16×C151 | Q8 | semidirect |
| 124. C151 | #3166 | semidirect |
| 176. M16 | Dic302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752765 | 2 |
| C2×#18012730 | 2 |
| #23752620 | 2 |
| #23752619 | 2 |
| #23752613 | 2 |
| #23752612 | 2 |
| #23752255 | 2 |
| #23752254 | 2 |
| #23752252 | 2 |
| M16×Dic151 | 2 |
| #428×C151 | 2 |
| #3166 | 151 |