Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 2. #23752620 | C2 | semidirect |
| 3. #23752618 | C2 | semidirect |
| 4. #23752616 | C2 | semidirect |
| 5. #23752614 | C2 | semidirect |
| 6. #23752613 | C2 | semidirect |
| 11. #500×C151 | C2 | semidirect |
| 42. #14558987 | Q8 | semidirect |
| 45. C8×D151 | Q8 | semidirect |
| 107. C151 | #3164 | semidirect |
| 113. #500 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752839 | 2 |
| #23752620 | 2 |
| #23752618 | 2 |
| #23752616 | 2 |
| #23752614 | 2 |
| #23752613 | 2 |
| #23752253 | 2 |
| #23752249 | 2 |
| #107×D151 | 2 |
| #23752166 | 2 |
| #500×C151 | 2 |
| #3164 | 151 |