Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #23750425 | C2 | semidirect |
| 2. C2×#18011937 | C2 | semidirect |
| 3. #23750192 | C2 | semidirect |
| 4. #23749643 | C2 | semidirect |
| 5. #23749598 | C2 | semidirect |
| 6. #23749396 | C2 | semidirect |
| 7. #418×C149 | C2 | semidirect |
| 40. C2×Dic298 | D4 | semidirect |
| 42. C2×D596 | D4 | semidirect |
| 55. #14558720 | D4 | semidirect |
| 71. C2×C8×C149 | D4 | semidirect |
| 142. C149 | #2008 | semidirect |
| 148. #418 | D149 | semidirect |
| 210. C2×C8 | C22⋊D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750425 | 2 |
| C2×#18011937 | 2 |
| #23750192 | 2 |
| #23749643 | 2 |
| #23749598 | 2 |
| #23749396 | 2 |
| #418×C149 | 2 |
| #2008 | 149 |