Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
| 2. #23750287 | C2 | semidirect |
| 3. #23750009 | C2 | semidirect |
| 4. #23749872 | C2 | semidirect |
| 5. #23749847 | C2 | semidirect |
| 6. #23749782 | C2 | semidirect |
| 7. #23749773 | C2 | semidirect |
| 8. #23749704 | C2 | semidirect |
| 9. C4×Q16×C149 | C2 | semidirect |
| 64. Q16×C149 | D4 | semidirect |
| 117. C149 | #3277 | semidirect |
| 126. C4×Q16 | D149 | semidirect |
| 170. Q16 | D596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011943 | 2 |
| #23750287 | 2 |
| #23750009 | 2 |
| #23749872 | 2 |
| #23749847 | 2 |
| #23749782 | 2 |
| #23749773 | 2 |
| #23749704 | 2 |
| C4×Q16×C149 | 2 |
| #3277 | 149 |