Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23752622 | C2 | semidirect |
| 4. #23752621 | C2 | semidirect |
| 5. #23752618 | C2 | semidirect |
| 6. #23752616 | C2 | semidirect |
| 7. #23752609 | C2 | semidirect |
| 11. #501×C151 | C2 | semidirect |
| 52. #14558987 | Q8 | semidirect |
| 95. C151⋊C8 | C2×Q8 | semidirect |
| 103. C8×C151 | C2×Q8 | semidirect |
| 124. C151 | #3165 | semidirect |
| 131. #501 | D151 | semidirect |
| 228. C8 | Q8×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752768 | 2 |
| C4⋊Q8×D151 | 2 |
| #23752622 | 2 |
| #23752621 | 2 |
| #23752618 | 2 |
| #23752616 | 2 |
| #23752609 | 2 |
| #23752253 | 2 |
| #23752251 | 2 |
| #23752164 | 2 |
| #501×C151 | 2 |
| #3165 | 151 |