Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 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. #23752516 | C2 | semidirect |
| 3. #23752509 | C2 | semidirect |
| 4. #23752499 | C2 | semidirect |
| 5. #23752494 | C2 | semidirect |
| 6. #23752255 | C2 | semidirect |
| 7. C2×#18012670 | C2 | semidirect |
| 8. #23752239 | C2 | semidirect |
| 11. #544×C151 | C2 | semidirect |
| 42. #14559004 | Q8 | semidirect |
| 123. C151 | #3084 | semidirect |
| 125. #544 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752692 | 2 |
| #23752516 | 2 |
| #23752509 | 2 |
| #23752499 | 2 |
| #23752494 | 2 |
| #23752255 | 2 |
| C2×#18012670 | 2 |
| #23752239 | 2 |
| #23752211 | 2 |
| #23752206 | 2 |
| #544×C151 | 2 |
| #3084 | 151 |