Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
276 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 85 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. #27132715 | C2 | semidirect |
| 3. C4×C8×D191 | C2 | semidirect |
| 4. Q8⋊(C191⋊C8) | C2 | semidirect |
| 5. #27132392 | C2 | semidirect |
| 6. #27132390 | C2 | semidirect |
| 7. Q8⋊C8×C191 | C2 | semidirect |
| 28. #15690288 | C8 | semidirect |
| 61. D764 | C2×C8 | semidirect |
| 78. Q8×C191 | C2×C8 | semidirect |
| 109. C191 | #1476 | semidirect |
| 115. Q8⋊C8 | D191 | semidirect |
| 170. Q8 | C8×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15690288 | 2 |
| #27132715 | 2 |
| C4×C8×D191 | 2 |
| Q8⋊(C191⋊C8) | 2 |
| #27132392 | 2 |
| #27132390 | 2 |
| Q8⋊C8×C191 | 2 |
| #1476 | 191 |