Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#18011943 | C2 | semidirect |
| 3. C4⋊Q8×D149 | C2 | semidirect |
| 4. #23750018 | C2 | semidirect |
| 5. #23750004 | C2 | semidirect |
| 6. #23749999 | C2 | semidirect |
| 7. #23749998 | C2 | semidirect |
| 8. C4×#14558719 | C2 | semidirect |
| 9. #494×C149 | C2 | semidirect |
| 46. #14558719 | D4 | semidirect |
| 89. C4×C149 | #137 | semidirect |
| 98. C149 | #3152 | semidirect |
| 105. #494 | D149 | semidirect |
| 191. C4 | #18011943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011943 | 2 |
| #23750176 | 2 |
| C4⋊Q8×D149 | 2 |
| #23750018 | 2 |
| #23750004 | 2 |
| #23749999 | 2 |
| #23749998 | 2 |
| C4×#14558719 | 2 |
| #494×C149 | 2 |
| #3152 | 149 |