Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 1. C2×#18011933 | C2 | semidirect |
| 2. #23750296 | C2 | semidirect |
| 3. #23750280 | C2 | semidirect |
| 4. #23749998 | C2 | semidirect |
| 5. #23749854 | C2 | semidirect |
| 6. #23749836 | C2 | semidirect |
| 7. #23749821 | C2 | semidirect |
| 8. #23749789 | C2 | semidirect |
| 9. #23749772 | C2 | semidirect |
| 10. C4×#14558725 | C2 | semidirect |
| 11. C8×D4×C149 | C2 | semidirect |
| 61. #14558725 | D4 | semidirect |
| 127. C4×C149 | #135 | semidirect |
| 140. C149 | #3284 | semidirect |
| 152. C8×D4 | D149 | semidirect |
| 272. C4 | #18011933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011933 | 2 |
| #23750296 | 2 |
| #23750280 | 2 |
| #23749998 | 2 |
| #23749854 | 2 |
| #23749836 | 2 |
| #23749821 | 2 |
| #23749789 | 2 |
| #23749772 | 2 |
| C4×#14558725 | 2 |
| C8×D4×C149 | 2 |
| #3284 | 149 |