Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23749938 | C2 | semidirect |
| 3. #23749920 | C2 | semidirect |
| 4. #23749825 | C2 | semidirect |
| 5. #23749764 | C2 | semidirect |
| 6. #23749723 | C2 | semidirect |
| 7. #23749682 | C2 | semidirect |
| 8. C2×C4×Q8×C149 | C2 | semidirect |
| 76. Q8×C149 | #41 | semidirect |
| 111. C149 | #3112 | semidirect |
| 114. C2×C4×Q8 | D149 | semidirect |
| 181. Q8 | #14558736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750175 | 2 |
| #23749938 | 2 |
| #23749920 | 2 |
| #23749825 | 2 |
| #23749764 | 2 |
| #23749723 | 2 |
| #23749682 | 2 |
| C2×C4×Q8×C149 | 2 |
| #3112 | 149 |