Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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×#18011856 | C2 | semidirect |
| 2. #23749866 | C2 | semidirect |
| 4. #23749453 | C2 | semidirect |
| 5. #23749430 | C2 | semidirect |
| 6. #23749427 | C2 | semidirect |
| 7. C22×C16×C149 | C2 | semidirect |
| 39. C16×C149 | D4 | semidirect |
| 59. C22×C149 | SD32 | semidirect |
| 75. C149 | #2217 | semidirect |
| 78. C22×C16 | D149 | semidirect |
| 115. C16 | C22⋊D149 | semidirect |
| 138. C22 | #18011856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18011856 | 2 |
| #23749866 | 2 |
| #23749861 | 2 |
| #23749453 | 2 |
| #23749430 | 2 |
| #23749427 | 2 |
| C22×C16×C149 | 2 |
| #2217 | 149 |