Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
336 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#20259253 | C2 | semidirect |
| 4. #27132426 | C2 | semidirect |
| 5. #340×C191 | C2 | semidirect |
| 9. C2×C8×D191 | C4 | semidirect |
| 48. C191⋊C8 | C22⋊C4 | semidirect |
| 67. C2×D191 | #106 | semidirect |
| 80. C191 | #1807 | semidirect |
| 86. #340 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D191 | 2 |
| C2×#20259253 | 2 |
| #27132520 | 2 |
| #27132426 | 2 |
| #340×C191 | 2 |
| #1807 | 191 |