Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #23750705 | C2 | semidirect |
| 2. #23750671 | C2 | semidirect |
| 3. #23750669 | C2 | semidirect |
| 4. D149⋊#108 | C2 | semidirect |
| 5. #23750624 | C2 | semidirect |
| 6. #23750588 | C2 | semidirect |
| 9. #18011999 | C22 | semidirect |
| 14. #18011982 | C22 | semidirect |
| 15. #18011981 | C22 | semidirect |
| 16. #18011976 | C22 | semidirect |
| 17. #18011965 | C22 | semidirect |
| 18. C8×#10597010 | C22 | semidirect |
| 20. #18011934 | C4 | semidirect |
| 21. #18011934 | C4 | semidirect |
| 24. C2×#14558723 | C4 | semidirect |
| 25. C2×D1192 | C4 | semidirect |
| 27. C2×Q16×C149 | C4 | semidirect |
| 101. C149 | #2957 | semidirect |
| 115. C2×Q16 | #10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750705 | 2 |
| #23750671 | 2 |
| #23750669 | 2 |
| D149⋊#108 | 2 |
| #23750624 | 2 |
| #23750588 | 2 |
| C2×#18011934 | 2 |
| #2957 | 149 |