Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #23750093 | C2 | semidirect |
| 3. #23749643 | C2 | semidirect |
| 4. C2×#18011838 | C2 | semidirect |
| 5. #23749395 | C2 | semidirect |
| 6. #23749384 | C2 | semidirect |
| 7. #410×C149 | C2 | semidirect |
| 9. #18011942 | C4 | semidirect |
| 11. #18011937 | C4 | semidirect |
| 46. #14558720 | C2×C4 | semidirect |
| 59. C2×Q8×C149 | C2×C4 | semidirect |
| 61. C2×D4×C149 | C2×C4 | semidirect |
| 129. C149 | #1906 | semidirect |
| 135. #410 | D149 | semidirect |
| 168. C2×Q8 | C4×D149 | semidirect |
| 172. C2×D4 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750423 | 2 |
| #23750093 | 2 |
| #23749643 | 2 |
| C2×#18011838 | 2 |
| #23749395 | 2 |
| #23749384 | 2 |
| #410×C149 | 2 |
| #1906 | 149 |