Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
394 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 179 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. Q8×#11924746 | C2 | semidirect |
| 3. #23749704 | C2 | semidirect |
| 4. #23749702 | C2 | semidirect |
| 5. #23749676 | C2 | semidirect |
| 6. #23749647 | C2 | semidirect |
| 7. C8×Q8×C149 | C2 | semidirect |
| 53. Q8×C149 | M16 | semidirect |
| 74. C149 | #2991 | semidirect |
| 78. C8×Q8 | D149 | semidirect |
| 118. Q8 | #14558719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14558737 | 2 |
| Q8×#11924746 | 2 |
| #23749704 | 2 |
| #23749702 | 2 |
| #23749676 | 2 |
| #23749647 | 2 |
| C8×Q8×C149 | 2 |
| #2991 | 149 |