Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752935 | C2 | semidirect |
| 2. #23752574 | C2 | semidirect |
| 3. #23752564 | C2 | semidirect |
| 4. #23752504 | C2 | semidirect |
| 5. #23752489 | C2 | semidirect |
| 7. #23752417 | C2 | semidirect |
| 8. #23752343 | C2 | semidirect |
| 9. #23752312 | C2 | semidirect |
| 11. D4×Q8×C151 | C2 | semidirect |
| 122. C151 | #3367 | semidirect |
| 125. D4×Q8 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752935 | 2 |
| #23752574 | 2 |
| #23752564 | 2 |
| #23752504 | 2 |
| #23752489 | 2 |
| #23752427 | 2 |
| #23752417 | 2 |
| #23752343 | 2 |
| #23752312 | 2 |
| C4×#14558989 | 2 |
| D4×Q8×C151 | 2 |
| #3367 | 151 |