Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#14558723 | C2 | semidirect |
| 3. C2×#18011835 | C2 | semidirect |
| 4. C2×#18011831 | C2 | semidirect |
| 5. C2×C22⋊#11924746 | C2 | semidirect |
| 6. #23749387 | C2 | semidirect |
| 7. C2×C22⋊Q8×C149 | C2 | semidirect |
| 46. C2×#11924746 | D4 | semidirect |
| 56. C2×Q8×C149 | D4 | semidirect |
| 69. C4⋊C4×C149 | D4 | semidirect |
| 94. C23×C149 | SD16 | semidirect |
| 157. C149 | #2000 | semidirect |
| 160. C2×C22⋊Q8 | D149 | semidirect |
| 194. C2×Q8 | C22⋊D149 | semidirect |
| 226. C4⋊C4 | C22⋊D149 | semidirect |
| 242. C23 | #14558723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558723 | 2 |
| C2×#18011885 | 2 |
| C2×#18011835 | 2 |
| C2×#18011831 | 2 |
| C2×C22⋊#11924746 | 2 |
| #23749387 | 2 |
| C2×C22⋊Q8×C149 | 2 |
| #2000 | 149 |