Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×Q16×D149 | C2 | semidirect |
| 3. #23750003 | C2 | semidirect |
| 4. #23749866 | C2 | semidirect |
| 5. #23749863 | C2 | semidirect |
| 6. #23749833 | C2 | semidirect |
| 7. #23749781 | C2 | semidirect |
| 8. #23749779 | C2 | semidirect |
| 9. Q16×Dic149 | C2 | semidirect |
| 11. C22×Q16×C149 | C2 | semidirect |
| 76. Q16×C149 | D4 | semidirect |
| 84. C22⋊D149 | Q16 | direct (N × H) |
| 112. C22×C149 | C2×Q16 | semidirect |
| 116. C2×D149 | C2×Q16 | semidirect |
| 126. Dic149 | C2×Q16 | semidirect |
| 132. C149 | D4×Q16 | semidirect |
| 135. C22×Q16 | D149 | semidirect |
| 193. Q16 | C22⋊D149 | direct (N × H) |
| 248. C22 | Q16×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D149 | 2 |
| Q8×C22⋊D149 | 2 |
| #23750003 | 2 |
| #23749866 | 2 |
| #23749863 | 2 |
| #23749833 | 2 |
| #23749781 | 2 |
| #23749779 | 2 |
| Q16×Dic149 | 2 |
| C8×C22⋊D149 | 2 |
| C22×Q16×C149 | 2 |
| D4×Q16 | 149 |