Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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×#18012761 | C2 | semidirect |
| 2. C2×#18012759 | C2 | semidirect |
| 3. #23752758 | C2 | semidirect |
| 4. #23752597 | C2 | semidirect |
| 5. #23752595 | C2 | semidirect |
| 6. #23752593 | C2 | semidirect |
| 7. #23752590 | C2 | semidirect |
| 8. #23752587 | C2 | semidirect |
| 9. #23752583 | C2 | semidirect |
| 10. C2×C8×Dic151 | C2 | semidirect |
| 11. C2×#135×C151 | C2 | semidirect |
| 55. C2×C151⋊C8 | D4 | semidirect |
| 74. C2×C8×C151 | D4 | semidirect |
| 119. Dic151 | #135 | semidirect |
| 125. C151 | #3147 | semidirect |
| 129. C2×#135 | D151 | semidirect |
| 194. C2×C8 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012761 | 2 |
| C2×#18012759 | 2 |
| #23752758 | 2 |
| #23752597 | 2 |
| #23752595 | 2 |
| #23752593 | 2 |
| #23752590 | 2 |
| #23752587 | 2 |
| #23752583 | 2 |
| C2×C8×Dic151 | 2 |
| C2×#135×C151 | 2 |
| #3147 | 151 |