Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
440 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 234 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. #23750674 | C2 | direct (N × H) |
| 23. C2×#11924753 | Q8 | semidirect |
| 27. C2×Dic298 | C8 | semidirect |
| 42. #11924753 | C2×Q8 | semidirect |
| 43. Dic298 | C2×C8 | semidirect |
| 68. C2×C149 | C8×Q8 | semidirect |
| 72. C149 | C2×C8×Q8 | semidirect |
| 141. C2 | #23750674 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750674 | 2 |
| C2×#18011978 | 2 |
| C2×C4⋊#11924753 | 2 |
| C2×C4×#11924753 | 2 |
| C2×#18011876 | 2 |
| C2×C8×Q8 | 149 |