Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
180 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #27132416 | C2 | semidirect |
| 5. #27132415 | C2 | semidirect |
| 6. #27132413 | C2 | semidirect |
| 7. #334×C191 | C2 | semidirect |
| 27. #15690270 | C8 | semidirect |
| 53. C191⋊C8 | C2×C8 | semidirect |
| 60. C8×C191 | C2×C8 | semidirect |
| 77. C191 | #1565 | semidirect |
| 85. #334 | D191 | semidirect |
| 138. C8 | C8×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27132715 | 2 |
| C4⋊C8×D191 | 2 |
| C4×#15690270 | 2 |
| #27132416 | 2 |
| #27132415 | 2 |
| #27132413 | 2 |
| #334×C191 | 2 |
| #1565 | 191 |