Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
398 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 168 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. #23750675 | C2 | semidirect |
| 2. #23750654 | C2 | semidirect |
| 3. D4×#11924753 | C2 | semidirect |
| 4. #23750646 | C2 | semidirect |
| 5. #23750644 | C2 | semidirect |
| 6. #23750629 | C2 | semidirect |
| 7. C2×C4⋊#11924753 | C2 | semidirect |
| 79. D4×C149 | M16 | semidirect |
| 107. C149 | #2990 | semidirect |
| 172. D4 | #14558746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750675 | 2 |
| #23750654 | 2 |
| D4×#11924753 | 2 |
| #23750646 | 2 |
| #23750644 | 2 |
| #23750629 | 2 |
| C2×C4⋊#11924753 | 2 |
| C4×#14558735 | 2 |
| #2990 | 149 |