Finite Group DatabasebetaFinite Group DatabasebetaOrder 5248.
628 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C41 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C41 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#124×C41 | C2 | semidirect |
| 2. C2×C4×D4×C41 | C2 | semidirect |
| 3. C41×#397 | C2 | semidirect |
| 4. C41×#393 | C2 | semidirect |
| 5. C41×#392 | C2 | semidirect |
| 6. C41×#392 | C2 | semidirect |
| 7. C41×#386 | C2 | semidirect |
| 8. C41×#383 | C2 | semidirect |
| 52. C42×C41 | D4 | semidirect |
| 102. #2631 | C41 | direct (N × H) |
| 109. C2×#124 | C2×C41 | semidirect |
| 110. C2×C4×D4 | C2×C41 | semidirect |
| 111. #397 | C2×C41 | semidirect |
| 112. #393 | C2×C41 | semidirect |
| 113. #392 | C2×C41 | semidirect |
| 114. #392 | C2×C41 | semidirect |
| 115. #386 | C2×C41 | semidirect |
| 116. #383 | C2×C41 | semidirect |
| 117. C41 | #2631 | direct (N × H) |
| 161. C42 | D4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#124×C41 | 2 |
| C2×C4×D4×C41 | 2 |
| C41×#397 | 2 |
| C41×#393 | 2 |
| C41×#392 | 2 |
| C41×#386 | 2 |
| C41×#383 | 2 |
| #2631 | 41 |