Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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. #23750635 | C2 | semidirect |
| 2. #23750624 | C2 | semidirect |
| 3. #23750623 | C2 | semidirect |
| 4. #23750606 | C2 | semidirect |
| 5. #23750605 | C2 | semidirect |
| 6. #23750588 | C2 | semidirect |
| 26. C2×#14558726 | C4 | semidirect |
| 27. C2×#14558725 | C4 | semidirect |
| 28. C2×#14558721 | C4 | semidirect |
| 30. C2×SD16×C149 | C4 | semidirect |
| 132. C149 | #1976 | semidirect |
| 149. C2×SD16 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750635 | 2 |
| #23750624 | 2 |
| #23750623 | 2 |
| #23750606 | 2 |
| #23750605 | 2 |
| #23750588 | 2 |
| C2×#18011932 | 2 |
| #1976 | 149 |