Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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. #41×#10597010 | C2 | semidirect |
| 2. #23750622 | C2 | semidirect |
| 3. C2×#18011975 | C2 | semidirect |
| 4. #23750605 | C2 | semidirect |
| 5. #23750508 | C2 | semidirect |
| 6. #23750497 | C2 | semidirect |
| 24. #18011944 | C4 | semidirect |
| 25. #18011941 | C4 | semidirect |
| 27. #18011937 | C4 | semidirect |
| 32. AGL(1,ℤ/8)×C149 | C4 | semidirect |
| 59. C2×Dic298 | C2×C4 | semidirect |
| 73. #14558720 | C2×C4 | semidirect |
| 77. C2×D4×C149 | C2×C4 | semidirect |
| 80. M16×C149 | C2×C4 | semidirect |
| 150. C149 | #1906 | semidirect |
| 166. AGL(1,ℤ/8) | #10597010 | semidirect |
| 199. C2×D4 | C2×#10597010 | semidirect |
| 217. M16 | C2×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#10597010 | 2 |
| #23750622 | 2 |
| C2×#18011975 | 2 |
| #23750605 | 2 |
| #23750508 | 2 |
| #23750497 | 2 |
| #23750421 | 2 |
| #1906 | 149 |