Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
162 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 61 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. #27132794 | C2 | semidirect |
| 4. #27132415 | C2 | semidirect |
| 6. #27132385 | C2 | semidirect |
| 7. Q8⋊C8×C191 | C2 | semidirect |
| 51. C191⋊C8 | M16 | semidirect |
| 77. C191 | #1592 | semidirect |
| 83. Q8⋊C8 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27132794 | 2 |
| C4×#15690274 | 2 |
| #27132740 | 2 |
| #27132415 | 2 |
| #27132392 | 2 |
| #27132385 | 2 |
| Q8⋊C8×C191 | 2 |
| #1592 | 191 |