Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23752840 | C2 | semidirect |
| 3. #23752577 | C2 | semidirect |
| 4. #23752572 | C2 | semidirect |
| 5. #23752567 | C2 | semidirect |
| 6. #23752559 | C2 | semidirect |
| 7. #23752218 | C2 | semidirect |
| 8. #23752214 | C2 | semidirect |
| 9. #23752209 | C2 | semidirect |
| 10. C2×#18012661 | C2 | semidirect |
| 11. #405×C151 | C2 | semidirect |
| 14. #18012739 | C22 | semidirect |
| 17. #18012731 | C22 | semidirect |
| 26. #18012664 | C22 | semidirect |
| 27. #18012664 | C22 | semidirect |
| 28. #18012664 | C22 | semidirect |
| 33. #18012661 | C22 | semidirect |
| 34. #18012661 | C22 | semidirect |
| 35. #18012661 | C22 | semidirect |
| 39. #97×C151 | C22 | semidirect |
| 40. C4×C8×C151 | C22 | semidirect |
| 135. C151 | #3136 | semidirect |
| 147. #405 | D151 | semidirect |
| 175. #97 | C2×D151 | semidirect |
| 176. C4×C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752840 | 2 |
| #23752781 | 2 |
| #23752577 | 2 |
| #23752572 | 2 |
| #23752567 | 2 |
| #23752559 | 2 |
| #23752218 | 2 |
| #23752214 | 2 |
| #23752209 | 2 |
| C2×#18012661 | 2 |
| #405×C151 | 2 |
| #3136 | 151 |