Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 2. C2×#18011911 | C2 | semidirect |
| 3. #23749998 | C2 | semidirect |
| 4. #23749976 | C2 | semidirect |
| 5. #23749831 | C2 | semidirect |
| 6. #23749766 | C2 | semidirect |
| 7. #431×C149 | C2 | semidirect |
| 72. C2×C4×C149 | SD16 | semidirect |
| 100. C149 | #3206 | semidirect |
| 108. #431 | D149 | semidirect |
| 173. C2×C4 | #14558725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| C2×#18011911 | 2 |
| #23749998 | 2 |
| #23749976 | 2 |
| #23749831 | 2 |
| #23749766 | 2 |
| #431×C149 | 2 |
| #3206 | 149 |