Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 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. #23752518 | C2 | semidirect |
| 4. #23752515 | C2 | semidirect |
| 5. #23752501 | C2 | semidirect |
| 6. #23752496 | C2 | semidirect |
| 7. C2×#18012670 | C2 | semidirect |
| 8. #23752240 | C2 | semidirect |
| 11. #428×C151 | C2 | semidirect |
| 42. #14559004 | Q8 | semidirect |
| 123. C151 | #3084 | semidirect |
| 131. #428 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752840 | 2 |
| #23752693 | 2 |
| #23752518 | 2 |
| #23752515 | 2 |
| #23752501 | 2 |
| #23752496 | 2 |
| C2×#18012670 | 2 |
| #23752240 | 2 |
| #23752214 | 2 |
| #23752206 | 2 |
| #428×C151 | 2 |
| #3084 | 151 |