Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23752509 | C2 | semidirect |
| 3. #23752509 | C2 | semidirect |
| 4. #23752499 | C2 | semidirect |
| 5. #23752489 | C2 | semidirect |
| 6. #23752252 | C2 | semidirect |
| 7. #23752248 | C2 | semidirect |
| 8. #23752239 | C2 | semidirect |
| 11. #544×C151 | C2 | semidirect |
| 21. #18012672 | C22 | semidirect |
| 22. #18012672 | C22 | semidirect |
| 23. #18012672 | C22 | semidirect |
| 24. #18012670 | C22 | semidirect |
| 25. #18012670 | C22 | semidirect |
| 26. #18012670 | C22 | semidirect |
| 27. C4⋊(C151⋊C8) | C22 | semidirect |
| 28. C4⋊(C151⋊C8) | C22 | semidirect |
| 34. C4⋊Q8×C151 | C22 | semidirect |
| 36. #125×C151 | C22 | semidirect |
| 44. C2×D604 | Q8 | semidirect |
| 124. C151 | #3081 | semidirect |
| 126. #544 | D151 | semidirect |
| 141. C4⋊Q8 | C2×D151 | semidirect |
| 143. #125 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752686 | 2 |
| #23752509 | 2 |
| #23752499 | 2 |
| #23752489 | 2 |
| #23752252 | 2 |
| #23752248 | 2 |
| #23752239 | 2 |
| #23752216 | 2 |
| C2×#18012659 | 2 |
| #544×C151 | 2 |
| #3081 | 151 |